Epic Black Hole Dispute Between Scientists

Physicist Stephen Crothers has demonstrated Hilbert’s derivation of the field equations is incorrect. Black hole physics violates SR, which means it also violates GR. Even by the mainstreams own standards, black holes are an impossibility. SR forbids infinite point mass particles such as a black hole singularity. Further, Schwarzschild’s original paper that proposed the solution to the Mercury orbit problem, from which the black hole is supposedly derived, is regular in all of space-time. This absolutely refutes the notion of black holes. Schwarzschild’s original paper in English can be found here. Hilbert’s solution to the field equations is erroneous.

Crothers undertook a long dialog with a Dr. Christian Corda, Editor-in-Chief of The Open Astronomy Journal, who freely admits that there is no such thing as black holes, but then refuses publication of Crothers’ papers based on ideological disagreements.

It is interesting to note that black hole “non-believers” include Einstein and Schwarzschild, yet their names are continually put forth as backers of this theory. Out of respect for their positions, the use of Einstein’s and Schwarzschild’s names in conjunction with these objects should cease immediately.

Some choice quotes from the dialog:

Again Steve, I suggest you change your way of proceed. I think that you are surely a talented researcher within gravitational physics, I agree with you that black-holes do not exist, but nobody will follow you if you insist to claim that not only the present community of gravitational physicists, but also the same Einstein, Schwarzschild, Hilbert, etc., i,e. the Founders Fathers of General Relativity, were wrong and the only correct person is Steve Crothers. in particular, be sure that I will NEVER follow you.

To summarize the dialog, Crothers pointed out that the equation scientists use in their formulation of black holes is wrong because it doesn’t actually give a boundary condition for the supposed edge of a black hole.

No boundary = no black hole.

The equation physicists use to describe the boundary of a black hole is totally arbitrary and is an artifact of a bad equation first formulated by one David Hilbert.

Crothers personal saga to see this error of physics corrected has led him into some absolutely insane confrontations. It is worth clicking his name to read all about it.

Watch Crothers explain the madness here:

Given that we now know black holes do not exist, you should all check out my site for further evidence that refutes Einstein’s nonsense.

Recently Stephen Hawking came out saying there is no such thing as a black hole.  To quote Nature:

Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape.

You see, when someone like Crothers says there is no valid black hole boundary, he is written off as a crank, but if Hawking says it, well it must be true! That’s how science is supposed to work!  It doesn’t matter what you can prove, it only matters who you are.

For those of you who want a layman’s explanation for what is really going on, watch this:

You can find supporting scientific papers for all of the claims made in the video by going here.

If you want more articles that detail what is really going on for the layman, look here.

  • Lulz

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  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • Lulz

    America collective turn away from god is a reason for state growth? Mr. Von Campe define your god because so far I’m sceptical that is unless freedom is your god ;)

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

  • http://aetherwavetheory.blogspot.com/ Zephir

    /** Black hole physics violates SR, which means it also violates GR.. **/

    This is not technically true, because SR doesn’t share postulate set with GR. It’s completelly different theory from this perspective and as such it could always violate it without any problem.

    Regarding the BH paradox, I presume redditors are more intelligent and they understand, the solution of (seeming) black hole (BH) paradox would depend on (exact) BH definition.

    For example – should all BH contain the singularity – or just the presence of event horizon is required there? If the event horizon is present, how can we test the presence of central singularity? And so on…

    • http://fascistsoup.com/ Michael Suede

      SR can not violate GR

      SR forbids infinite point mass particles; therefore ipso facto, GR forbids infinite point mass particles.

      • http://profiles.google.com/pskeptic Paranormal Skeptic

        SR nor GR forbid infinite point mass particles.  They simply lead to undefined results.

        It’s like saying one can not get the square root of a negative number.  But we can, hence imaginary numbers.

        • New_Idiot

          One deep idea in Special Relativity is that faster than light is impossible. Well, the infinite point mass singularity at the centre of black holes violates it, ie to move faster than light you need infinite energy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVitte’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/paper.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

  • Christian Corda

    Dears readers,

    it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements. I refused publication of Mr. Crothers’ papers because I am absolutely sure that such papers are totally wrong from both of the physical and mathematical points of view.
    I showed correct physical and mathematical arguments on the potential non-existence of black holes, and, in general, of singularities, see my papers Mod. Phys. Lett. A2, 2423-2429 (2010) and Astropart. Phys. 3, 587-590 (2011). Such arguments have nothing to do with Mr. Crothers’ unscientific and totally wrong claims.
    On the contrary, I think that the confusion realized by Mr. Crothers and friends is favourable to people who claim on the existence of black holes and of singularities. In my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong.
    There is not a conspiracy of the Scientific Community against Mr. Crothers, merely Mr. Crothers does not understand Differential Geometry and General Relativity.
    Even if it is correct that Einstein was a black hole “non-believer” it is false that Schwarzschild was a black hole “non-believer” too. Unfortunately, Schwarzschild died some months after finding his solution to Einstein Field Equation, while the concept of “frozen star” (the term black hole was introduced only in 1964 and was due by A. Ewing in a letter to the American Association for the Advancement of Science) was introduced about 15 years after. On the other hand, Einstein’s argumentations on the non-existence of black holes had nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
    Notice also that Mr. Crothers has been very incorrect as he put in the web our private conversation without my permission.

    Christian Corda

    • http://fascistsoup.com/ Michael Suede

      Thanks for your input, if you are indeed Dr. Corda.

      I believe you are, and I also believe what you wrote is true from your perspective.

      However, I think we can all agree that there are no solutions to Einstein’s field equations that allow for the existence of more than one black hole per “mathematical universe.”

      Therefore any argumentation that takes place about black holes actually existing in “real life” must first address how it is possible for more than one black hole to actually exist within a given universe.

      Further, I think we can also all agree that when it comes to proposed theories that explain galactic rotation rates, jets, and other celestial objects that invoke singularities, deference must be given to those theories that do not invoke highly speculative objects that can not be verified through laboratory experimentation.

      Such as Anthony Peratt and Hannes Alfven’s theories of galaxy formation.

      • Cordac Galilei

        Dear Michael Suede,

        what do you mean with “mathematical universe”?
        Actually, there exist various mathematical solutions to Einstein’s field equations that allow for the existence of black holes in our Universe. The key point is that if such solutions exist in the physical reality too. A serious scientific argument is the Strong Principle of Equivalence (SPOE). In General Relativity the Einstein equation relates the curvature tensor of spacetime on the left hand side to the energy-momentum tensor in spacetime on the right hand side. Within the context of the Einstein equation the SPOE requires that special relativity must hold locally for all of the laws of physics in all of spacetime as seen by time-like observers. Hence, in the context of the SPOE
        this implies that the frame of reference of co-moving observers within a gravitationally collapsing object are required to always be able to be connected to the frame of reference of stationary observers by Special Relativistic transformations with physical velocities which are less than the speed of light. Recently plausible arguments have been made which support the idea that physically acceptable solutions to the Einstein equation will only be those which preserve the SPOE as a law of nature in the universe, see the works by my friends D. Leiter, S. Robertson, R. E. Schild in Astrophys. J. 596, L203 (2003), Mon. Not. Roy. Astron. Soc. 50, 1391 (2004), Astron. J. 2, 420 (2006). Such solutions do not admit event horizons and singularities. This is a correct way to proceed which is connected with Einstein’s argumentations on the non-existence of black holes. Once again, this point of view has nothing to do with Mr. Crothers’ unscientific and totally wrong argumentations.
        Sincerely,
        Christian Corda

        • http://fascistsoup.com/ Michael Suede

          “what do you mean with “mathematical universe”?”

          http://www.sjcrothers.plasmaresources.com/McVittie.pdf

          But that aside, I wouldn’t call Crothers work “unscientific.” It is important to remember that just because you can create a mathematical theory in which the bending of space is invoked to explain astrophysical observations, it does not mean that is what is actually occurring out there in space.

          Let us not forget that astrophysical plasma is electrically conductive and must obey circuit laws. Invoking bending space as a mechanism to explain configurations of charged plasma seems a bit presumptuous to me.

          Even if it can be demonstrated mathematically and empirically in the lab (which it hasn’t) that space actually bends and that the mathematical theories are entirely plausible, it is the MOST plausible theory that should be given the greatest consideration.

          Which is more plausible?

          1. That space bends itself into an infinitely dense point mass particle which powers AGN jets

          or

          2. Taking the known behavior of charged plasma in the laboratory and deducing a circuit theory mechanism for the observed behavior of AGN jets

          See a simple circuit theory of AGN jets here:

          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf
          http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf

          Black holes are not required Dr. Corda. Do not fool yourself into thinking that abandoning the black hole will leave us with no plausible answers.

          • Cordac Galilei

            Dear Michael Suede,

            I am not interested in philosophic discussions. The MOST plausible theory is the one which is better consistent with various astronomical observations. Even if I think that black holes could not exist, the theory which is better consistent with various astronomical observations, at the present time, is surely General Relativity than the known behavior of charged plasma.
            On the other hand, Crothers’ unscientific claims does explain nothing on astronomical observations.
            That is all, the rest is debating on nothing and I am not interested on it.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Your lack of interest in philosophic discussions is unsurprising.

            Obviously any GR theoretical description of an astrophysical object would be wrong if it does not conform to the known properties of charged plasma.

            I noticed you didn’t respond to the claims made in McVittie’s paper either. This is also unsurprising.

          • Christian Corda

            Dear Michael Suede,

            I didn’t respond to the claims made in McVittie’s paper merely because I have not time to read it. In any case, you insist with the black holes issue. This is not the point, even if I agree with yours and Mr. Crothers’ idea that black holes could not exist, but I use science, not ideology, I do not agree with your point of view on the un-correctness of GR. I read Mr. Crothers’ papers, there is so much nonsense in them that I am absolutely sure that Mr. Crothers understands nothing on GR. You and Mr. Crothers should be more modest. I lost more than 12 years in try to learn GR and I think I learnt, maybe, the 5-10% of this beautiful theory. Mr. Crothers started to study GR in 2003 and in few months he arrived to claim that black holes do not exists. More, in a couple of years he arrived to claim that the whole GR is wrong. This is absolutely ridiculous and arrogant.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            You do a lot of talking and not a lot of proving.

            How about you link me some papers that refute McVitte and Crother’s claims.

            I really don’t care how arrogant you think they are. I only care if they are correct or not. As far as I can tell, they are correct.

          • Christian Corda

            Dear Michael Suede,

            I regret but you are not correct.
            I previous linked you on my paper arXiv:1010.6031, accepted for publication in Electronic Journal of Theoretical Physics, where I have shown that Mr. Crothers’ argumentation on the fact that Schwarzschild’s original paper refutes the notion of black holes is totally wrong. Concerning the others nonsenses by Mr. Crothers, I signal you that Dr. Jason Sharples has published a paper in ‘Progress in Physics’, “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” which points out some of the many strange errors that Mr. Crothers makes in his somewhat bizarre and totally wrong interpretation of relativity.
            In all honesty, if Mr. Crothers’ argumentations are correct as you claim, I am Spider Man…
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I have read the “Coordinate Transformations and Metric Extension” paper which demonstrates that the original Schwarzschild solution is an extendible metric. However this paper does not get at the root of Crothers’ arguments, which are:

            1. That r strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime.

            and

            2. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes.

            You repeatedly claim Crothers’ physics is decidedly “strange”, “bizarre”, “nonsense”, “ridiculous” etc.. etc.. while at the same time you yourself are propounding that space itself (which is nothing) has physical properties that allow it to bend into an infinitely dense point mass object (which by definition is in violation of SR).

            Sir, I do not believe it is Crothers’ arguments which are “bizarre.”

          • Christian Corda

            You repeatedly and falsely claim that I propound that the space has physical properties that allow it to bend into an infinitely dense point mass object. This is absolutely false and shows that you did not read my post on the Strong Equivalence Principle. I regret, but I cannot continue a discussion with a person who does not read my fundamental point on this issue.
            Thus, this is my last post here.
            Good luck to you and Mr. Crothers for your unscientific nonsenses.
            Best regards,
            Ch.

            P.S.
            Notice that there not exist a GR textbook where it is claimed that the Schwarzschild radial coordinate denote any distance whatsoever in “Schwarzschild” spacetime. This is a false statement that Mr. Crothers uses as he does not understand the meaning of coordinates in GR. On the contrary, the name “radius” to the r coordinate in Schwarzschild geometry is ALWAYS used with great caution. Also notice that in a spherical line element in a Euclidean (flat) 3-dimensional space the metric radius and the Gaussian curvature are not equal too and are not required to be equal. Thus, the argument of Mr. Crothers that the Schwarzschild radial coordinate strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime means absolutely nothing.

          • http://fascistsoup.com/ Michael Suede

            That fact that it doesn’t denote an actual physical distance is the the entire point of Crothers argument.

            There is no “event horizon”

            Further, don’t get mad at me. Just provide me with an existence theorem that demonstrates more than one black hole can exist.

          • Christian Corda

            That fact that it doesn’t denote an actual physical distance is only an opinion by Mr. Crothers. Hence, if this is the entire point of Mr. Crothers argument this is a further confirmation that Mr. Crothers speaks nonsense. Your and Mr. Crothers should carefully study the meaning of coordinates in GR before further discussing on this theory.

          • Christian Corda

            I wrote a typo above. The correct sentence was
            “That fact that it doesn’t denote an actual physical distance is NOT only an opinion by Mr. Crothers.”
            In fact, the real physical distance is an integral on dr(1-rg/r)^-1/2 being rg the gravitational radius. Therefore, by claiming that r doesn’t denote an actual physical distance Mr. Crothers got there a bit late, didn’t he?

          • http://fascistsoup.com/ Michael Suede

            The text book definition of the Schwarzschild radius is that it represents the ability of mass to cause curvature in space and time.

            If you agree to this text book definition, then by default you believe that nothing has physical properties which can act upon something.

            It is illogical to say that space is nothing but a volume in which matter exists and at the same time say space is something which has measurable physical properties that can act upon matter.

            If you say that space itself (which is nothing) has physical properties that can act upon matter, then you must be able to demonstrate experimentally why this should be so.

            Given that there exist no laboratory experiments which can prove that space is more than nothing, all of this debate about bending space is academic and pointless. Observations of astrophysical objects alone are inconclusive given that there are numerous alternative explanations for those observations that do not invoke the bending of nothing. For example: plasma self-focusing, dynamic multiple scattering, CREIL effects, Wolf effects, etc..

            Further, your refusal to respond to McVittie’s existence theorem problem while engaging in ad hom attacks against myself and Mr. Crothers isn’t going win me or anyone else over to your viewpoints.

            I am a software developer, which means by definition I think logically. Logic is first and foremost what I adore in any theory. Any theory that is illogical is most likely wrong. While GR is a beautiful mathematical theory, it is predicated on some completely illogical assumptions about the fundamental properties of our universe. It also ignores half of what man knows to be true about the universe, which is that space plasma obeys electrodynamic laws as well as gravitational laws. As I just demonstrated, it also assumes that nothing can act upon something.

            If it is not space which bends, but in fact gravity is a wave property of matter in an electrodynamic sense (which would make sense and provide a mechanism with which one could produce a unified theory), then there are no black holes.

            But let us get back to this supposed radius. There are no papers that show r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

            Given that this statement is indeed true, even if we assume that nothing actually has properties that can act upon something, there still is no real radius of an event horizon that can be formulated.

            Further, given that division by zero is not allowed in SR, there can be no matter that exists in the form of a singularity and still be in agreement with SR.

            If you want to claim that black holes actually exist, then it must be demonstrated in SR that matter can actually take the form of having zero spatial extent.

            Of course, this too is impossible.

          • Stephen J. Crothersmis

            Corda had our correspondence withdrawn from the vixra site, exercising his copyright to his emails to me. He has denied me thereby right of reply to his invalid arguments. I will soon post the correspondence with Corda to my own site for all to see. He claims that I know no differential geometry. This is false. Go here for my pertinent mathematical papers:

            http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

            http://www.sjcrothers.plasmaresources.com/Reply-short.pdf

            The latter paper is my reply to Sharples.

            The proponents of the black hole make much fanfare of the quantity r that appears in the so-called “Schwarzschild solution”. They treat this issue with complicated mathematics and thereby confuse those not versed in the relevant mathematics. They routinely claim that this r is the radius, one way or another. However, this is false because it is not even a distance in “Schwarzschild” spacetime since it is easily proven that it strictly plays the role of the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime and so does not itself denote any distance whatsoever in “Schwarzschild” spacetime. Now one does not even need to understand the abstruse mathematics surrounding this issue to see that the black hole is invalid, making this complicated mathematical matter irrelevant, as I now show.

            According to the proponents of the black hole it has an escape velocity of that of light in vacuum. This is easily verified by reference to the relevant literature. Now if that is so then light can escape since it travels at the escape velocity and so all observers can “see” the black hole. Not only that, ponderable bodies could leave the black hole but not escape since according to the Theory of Relativity no ponderable body can acquire the speed of light in vacuum. So there is always a class of observers that can see these ponderable bodies leave and fall back to the black hole. On the other hand, the very same astrophysical scientists claim that neither light nor ponderable bodies can even leave the event horizon of the black hole. Thus, the black hole has no escape velocity. They also claim that there is no class of observers that can see the black hole, no matter how close the observers are to the event horizon. But escape velocity does not mean that objects cannot leave, only that they cannot escape. Thus, the astrophysical scientists maintain two contradictory claims, and so their arguments are invalid.

            Now all black hole “solutions”, be they for spinning or not, pertain to a universe that contains only one mass, the black hole itself. There are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be even asserted that his field equations contain latent solutions for multiple masses. The Principle of Superposition does not apply in General Relativity and so one cannot assert that black holes can persist in multitudes. All talk of black holes existing in multitudes, interacting with one another and other matter is due to thoughtlessly applying the Principle of Superposition where it does not apply. In Newton’s theory the Principle of Superposition applies and so one can pile up as many masses as one pleases in a given space, because space and matter are not causally linked, although the equations describing their gravitational interaction quickly become intractable. In General Relativity this is not possible because matter and spacetime are causally linked and so act upon one another. This means that each and every different configuration of matter requires its own specific solution. Furthermore, escape velocity is an a priori two-body relation: one body escapes from another body. But the black hole has no other body that can escape from it since it is allegedly in a universe that contains no other masses. In addition, there can be no observers in the spacetime of the black hole because observers are material, yet according to the proponents of the black hole observers and much other matter miraculously appear from nowhere. Upon what solution to the field equations do they rely for multiple masses? None!

            The black hole was spawned from a solution for the “field equations” Ric = 0, which is a spacetime that by construction contains no matter. This black hole is called the “Schwarzschild” black hole, even though it is not even Schwarzschild’s solution and that Schwarzschild’s actual solution contains no black hole. Consider another “Schwarzschild” black hole. It comes from the very same solution for the first “Schwarzschild” black hole. Therefore each is located in a universe that contains no other masses, by construction. Proponents of the black hole claim that such black holes can exist in binary systems and are located at the centres of galaxies and interact with other matter in the galaxies. They also claim that these black holes can collide and merge. But this is impossible because it is already an application of the Principle of Superposition where the Principle of Superposition does not apply! Consider the notion of two “Schwarzschild” black holes interacting with one another, as one finds in the literature. Then the two black holes mutually persist in and mutually interact in a mutual spacetime that by construction contains no matter! This is impossible. Similarly, there can be no masses other than black holes in the spacetime of some given black hole and thus nothing for it to interact with.

            According to black hole theory it takes an infinite amount of “outside” observer time for a body to reach the event horizon of a black hole. But nobody has been and nobody will be around for an infinite amount of time to make the observation. Thus the event horizon has no meaning in physics. Not only that, from where did the falling body and the observer miraculously appear, bearing in mind that there are no other masses in the spacetime of any given black hole? They come from again thoughtlessly applying the Principle of Superposition where the Principle of Superposition does not apply.

            The proponents of the black hole make use of a test particle, but inadequately define what a test particle is. Let a test particle be a very small mass, as many proponents of the black hole claim. It is asserted that this can be done because the test mass is so small that it has no appreciable effect on the gravitational field involving the black hole. But if the test particle is massive, no matter how small initially, it can, by the laws of Special Relativity, become arbitrarily large, but finite, as it “falls” in the gravitational field of the black hole and hence results in a significant mass in the allegedly empty spacetime of the black hole. This is a two-body problem, but as we have seen there are no known solutions for two or more masses and no existence theorem by which the notion can be justified. If the test particle is not massive it is meaningless.

            According to Einstein and his followers his Principle of Equivalence and his “laws” of Special Relativity must manifest in sufficiently small regions of his gravitational field and that these regions can be located anywhere in his gravitational field. Now both the Principle of Equivalence and the “laws” of Special Relativity are defined in terms of the a priori presence of multiple arbitrarily large finite masses and photons. Therefore it is impossible for the Principle of Equivalence and the “laws” of Special Relativity to manifest in a spacetime that by construction contains no matter. But Ric = 0, from which the “Schwarzschild” black hole is allegedly obtained, is a spacetime that by construction contains no matter. That is why Ric = 0 is called the static vacuum (i.e. empty) field equations. Thus Ric = 0 violates the physical principles of General Relativity and so is inadmissible and so the “Schwarzschild” black hole is again invalid.

            The proponents of the black hole remove all matter, including sources, by setting Ric = 0. They then prepare the ground for the presence of a source by next saying that Ric = 0 describes the gravitational field “outside a body”. They remove all matter at the outset by setting Ric = 0 and immediately put a mass back in with the words “outside a body”. This is a subtle but circular argument and is therefore invalid. Now, when they get their “Schwarzschild solution” there is no matter present in the solution. To satisfy their “outside a body” they have to put a massive body into the solution. They do this by a post hoc insertion of the square of Newton’s expression for escape velocity. But as we have seen Newton’s escape velocity is an a priori two-body relation (one body escapes from another body) and so it cannot rightly appear in what is alleged to be an expression for a universe that contains only one mass. Thus mass is inserted into the “Schwarzschild” solution by sleight of hand. Not only that, the denominator of Newton’s expression for escape velocity is a true radius but it is not even a distance in “Schwarzschild” spacetime, let alone the radius therein.

            It is also claimed that the black hole contains an infinitely dense point-mass singularity. Now a simple calculation using Special Relativity shows that Special Relativity forbids infinite density. Recall that Special Relativity must hold in sufficiently small regions of Einstein’s gravitational field. Therefore, there can be no infinitely dense point-mass singularity in Einstein’s gravitational field. Furthermore, a point is a mathematical object, not a physical object. It therefore cannot be massive or infinitely dense. In Newton’s theory there are infinitely dense point-masses too. They are called centres of mass. A centre of mass is not a physical object, merely a mathematical artifice. One can go to the store and buy a bag full of marbles but one cannot go to the store and by a bag full of centres of mass of the marbles. The proponents of the black hole claim that their infinitely dense point-mass singularities are physical objects. That is invalid too. The black hole is allegedly formed by irresistible gravitational collapse. Nobody has ever observed an astronomical body undergo gravitational collapse into zero volume and there is not one shred of laboratory evidence to suggest that masses can undergo such a process.

            The signatures of a black hole are an event horizon and an infinitely dense point-mass singularity. Nobody has ever found an event horizon or an infinitely dense point-mass singularity and so nobody has ever found a black hole, despite the now almost daily claims for black holes being found in multitudes, all over the place. Note once again that the multitude involves an application of the Principle of Superposition where the Principle of Superposition does not apply. All claims for the discovery of black holes are wishful thinking, not science.

            Black hole proponents often claim that the Michell-Laplace dark body from Newton’s theory is a kind of black hole. The Michell-Laplace dark body of Newton’s theory is theoretical. Nobody has ever found one of them either. Note however that the Michell-Laplace dark body is not a black hole: it has an escape velocity whereas the black hole does not have an escape velocity (see above); there is always a class of observers that can see the M-L dark body but according to the relativists there is no class of observers that can see the black hole; the dark body exists in a universe full of matter whereas the black hole is alone in the universe; the black hole has an event horizon, but the M-L dark body has no event horizon; the black hole has an infinitely dense point-mass singularity, but the M-L dark body does not; the black hole is created by irresistible gravitational collapse but the M-L dark body is not so created. Thus, the M-L dark body does not possess the signatures of a black hole and so it is not a black hole.

            Stephen J. Crothers

          • Christian Corda

            Mr. Crothers, you speak idiocies. You confuse Freedom in Science with writing totally wrong and unscientific claims. You are a very very unfair person as you: 1) sent our email correspondence to other people without my permission; 2) posted our whole email correspondence in the vixra site without my permission.
            As you always bore the Scientific Community with great social concepts like “right of reply” or “Freedom in Science” you has to learn that another important social concept is the RIGHT OF PRIVACY and you violated my right of privacy in a very shameful way.
            On the other hand it is totally false that by exercising my copyright to my emails to you I denied you thereby right of reply. You are absolutely free to put a lowest reply to my paper arXiv:1010.6031 in the vixra site without citing our privacy correspondence. More, you are absolutely free to send your lowest reply to my paper to a peer reviewed journal, but, as SURELY the reviewers will reject it because it will consist in a collection of unscientific claims, you should stop to bore people by claiming that your right of reply is denied. Merely and correctly, the Scientific Community thinks that you are a crank who understands nothing on General Relativity and Differential Geometry.
            More, I have been recently informed that you now endorse the unscientific pseudo-theory by Mr. M. Evans and the totally ridiculous, wrong and false claims on the incorrectness of Special Relativity by Mr. A. Sharma. This fact gives you an infinite credibility gap. I strongly suggest you and your friends to study and to learn theories before attacking them.
            This is my last reply to you because I lost even too much time in this cheerless discussion.
            Best regards,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            Calling people idiots and complaining about privacy rights is unbecoming a real scientist.

            Science is supposed to be done out in the open and people are supposed to criticize each others work.

            Please provide us with a multiple black hole existence theorem, explain why matter can take the form of having zero spatial extent according to SR, and provide papers where r denotes something more than inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of “Schwarzschild” spacetime.

          • Christian Corda

            Dear Mr. M. Suede,

            please stop to bore me by falsifying my sentences. I said that Mr. Crothers speaks idiocies, not that he is an idiot. Even intelligent people can speak idiocies sometimes.
            I am not interested to discuss General Relativity with a software developer. I do not bore you in lowest discussions on informatics because informatics is not my job. Hence, be modest and please stop to bore me with unscientific claims on General Relativity. You have your job, I have mine, that is all. If you will obtain a Ph.D in Mathematical Physics and you will publish papers on General Relativity in serious journals I will consider to discuss with you on black holes. I am not interested to further discuss with you and Mr. Crothers. Both of you have to study and to learn theories before attacking them.
            Best wishes,
            Ch.

          • http://fascistsoup.com/ Michael Suede

            I’ll assume by your reply that you are incapable of answering our criticisms because our criticisms are entirely valid.

            How do you feel when you look at yourself in the mirror in the morning knowing that your entire job is to sell the public lies so you can continue taking their money?

            Unlike priests and rabbi’s who get their money by voluntary donations, you get your paycheck primarily from public funding. Which means people don’t have a choice about giving you their money, even if they completely disagree with you.

            Shame on you.

          • http://www.facebook.com/ralph.huntington Ralph Huntington

            “I am not interested to discuss General Relativity with a software developer.”

            Such is the statement of a snob, not a scientist. One wonders if the vaunted academic would deign to discuss Relativity Theory with a postal worker.

          • http://www.facebook.com/octavian.popil Octavian Popil

            Dear Mr. Corda,
             
            I would like to thank you for taking the time to enlighten us about the way peer review really works. We’ve heard complaints from famous „cranks” now and then, but you offered us a glimpse from within the system. After reading all your posts here, I am now fully convinced that all the criticism which peer-review has taken over the years is not only justified, but not nearly as harsh as it needs to be!
             
            The highlight of your replies has been the first sentence: “it is not correct that I refused publication of Mr. Crothers’ papers based on ideological disagreements.” If you had stopped there, it would’ve been believable and appearances could have been saved. But by continuing, you have unwittingly exposed the real motivation behind peer review, which has a lot more to do with authority and selfishness than it has to do with competence and objectivity.
             
            According to your own account, you have lost 12 years trying to learn GR and you think you have learned „maybe 5-10% of this beautiful theory”. This is an admission of monumental incompetence, which means you are driven in your actions by belief, not knowledge. If you know it would take you 120-240 years to fully learn this „beautiful” theory, then you should also know that you have absolutely no competence to judge how well others understand it after only 12. years of learning If they may actually understand 100% in just a few years, how would you be able to realize it, if you only understand 5-10% in 12 years?! Further more, how can you judge that a theory is „beautiful” if you have not even understood it yet?! Your opinion on relativity is obviously based on an irrational belief in it, since you lack a complete understanding of it.
             
            By actually making judgements about other people’s work on something you do not understand yourself, you are proving that you have a cognitive bias known as the „Dunning–Kruger effect”, in which unskilled people (by your own admission) make poor decisions and reach erroneous conclusions, but their incompetence denies them the metacognitive ability to recognize their mistakes, and therefore the unskilled people suffer from illusory superiority, rating their ability as above average, much higher than it actually is.
             
            After exposing your own incompetence, you conclude that you are not interested in philosophical discussions with people who might actually BE competent, but you wouldn’t be able to see it (by the way, philosophy literally means „love of wisdom” and implies  a systematic approach and reliance on rational argument). People who are of different opinions than your own are „boring” you and any claims that they make are „unscientific” because they contradict your own and your peer reviewers, which are, of course, „scientific” claims by default, because you are „professional” scientists (as in it’s your job). So is this the bottom line of peer reviewing: protecting job security?! You surely make it look that way!
             
            By engaging in this discussion, you have given a lot of us one more reason to doubt the establishment „consesus” by peer review, and encouraged us to actually pay even closer attention to some of these so-called „cranks”. I think the expectation of many of us is that, most likely, it will be just one of these „cranks” that will come up with the solution for this huge gap in understanding of nature, not the establishment, which doesn’t even acknowledge this gap!
             
            Thank you again, for all your efforts. :)

          • J. Sharples

            I would like to point out an example of Mr Crothers unscientific conduct, which, as such, makes him a hypocrite. After publishing my “Coordinate Transformations and Metric Extensions” paper, my Head of School (i.e. my boss) received a letter insisting on my dismissal for criticising Crothers’ work. The letter was from one of Crothers’ cronies and demonstrates a desperate attempt to “play the man” rather than “play the ball” which he is unqualified to do.

            My Head of School found the letter quite amusing.

            Cheers,
            Jason

          • http://www.libertariannews.org/ Michael Suede

            So you believe that an infinitely dense point mass particle exists, which is in violation of special relativity?

            And you believe this because, rather than seeing matter being sucked into a “black hole,” we witness massive discharges of matter across galactic scales emanating from the center of AGNs?

            Perhaps you believe that galactic formation models under GR would be impossible without black holes, therefore they must be real – even if physicists have to throw in fake matter and energy on top of the black hole postulate to make their models work?

            You say Crothers is engaged in “unscientific conduct” – I say you are engaged in ramming a religion down the public’s throat with no good evidence to support your nonsense.

          • J. Sharples

            Dear Michael,

            Of course you are entitled to your say, but as I said, we should try and stick to the mathematics – that is where Crothers makes his errors. It is his interpretation of the spherically symmetric solution to the Einstein equations that is at issue. Whether an infinitely dense point mass exists as a physical reality or not is irrelevant – in fact the question lies outside GR. Please also note that the existence of *any* mass violates special relativity – that is why the general theory was required.

            I’m not sure how you see me as trying to “ram a religion down the public’s throat”, since I only respond in the literature and in a few of these “specialist” blogs where Crothers has tried to forward his own misguided musings. Crothers conduct, from the outset, is quite clearly unscientific.

            Best,
            J.

          • http://www.libertariannews.org/ Michael Suede

            “we should try and stick to the mathematics”

            Mathematics without a framework of logic and reason within which to interpret the results is useless.  There was a reason why natural philosophy played such a large role in cosmology prior to the 20th century.  

            The question is not whether you can create numerically valid models within Einstein’s relativity that match observation, the question is whether Einstein’s relativity is the best answer to what we observe.  

            Clearly there are much simpler solutions to what we observe that are not predicated on things like black holes, dark matter, dark energy, wimps, machos, multiple dimensions, gravitational waves, god particles, etc.. etc.. etc..   Therefore, since alternative explanations exist that better match the data, Occam’s razor demands that those theories take precedence over Einstein’s.

            A paper I wrote on this:

            http://knol.google.com/k/michael/einstein-was-wrong-falsifying/31bvt2170ijjb/1#

          • J. Sharples

            Dear Michael,

            The question, as I have stated already, is about Crothers’ interpretation of the mathematical solution of the Einstein equations under the assumption of spherical symmetry.  This is what your article at the top of this page is about. The other bits you mention are irrelevant to this discussion.

            Also, you say that “mathematics without a framework of logic and reason… is useless” What framework do you refer to? Are you not aware that mathematics itself is the closest we have to such a framework?!

            Finally, with regard to your comments on parsimony… Einstein’s theory is not predicated on black holes, dark matter, etc. Einstein’s theory is “G=T” – what could be simpler….?

          • http://www.libertariannews.org/ Michael Suede

            I think they are entirely relevant to the discussion.  You can supposedly provide math that will validate the existence of a black hole based on Hilbert’s derivation of the field equations – I say so what?

            What if the assumptions Hilbert made are wrong?  Since we don’t know what gravity is, what causes it, how to shield it or how to manipulate it, it strikes me as a bit presumptuous to conclude that gravity can manipulate space and time in the manner prescribed by Hilbert’s “black hole”.

            It also strikes me as ridiculous that GR ignores everything electrical in its interpretation of the cosmos.  It assumes that gravity is the only force of any consequence, when our radio telescopes tell us a very different story.

            When you make the assumption that space and time can be combined and distorted by an unknown force such as gravity in the manner prescribed by Hilbert, there are no cosmological observations that could ever falsify the theory.  For example, make up a cosmological observation in your mind that would entirely invalidate General Relativity.  I’ll bet you can’t do it because Einstein’s theory allows for any configuration of space and time, and for those observations that don’t work out, physicists simply throw in fake matter and energy to plug the holes.

            When you have dark matter, dark energy, black holes and bending space at your disposal, there are no observations that can not be explained away.  Clearly this does not mean the explanations are VALID anymore than Ptolemy’s epicycles were valid. 

            Just because you can use trickery in a mathematical equation to make it balance by bending space and time, that does not mean the model reflects reality in anyway what-so-ever.  GR is exactly like Ptolemy’s cosmology.  It is not predicated on science, it is nothing more than mathematical modeling clay for numbers geeks.  It explains nothing.

          • J. Sharples

            Again, the discussion is about the mathematical solution of the Einstein equations. There is no “supposedly” about the mathematics. The mathematics is absolutely concrete. Crothers’ interpretation is incorrect.

            The discussion is about Crothers’ claim that he has demonstrated that Hilbert’s derivation of the solution is wrong. This claim is false.

            Please try to stay on the point of the discussion.

            “GR is not predicated on science, it is nothing more than mathematical modelling clay for number geeks” – Classic!

          • http://www.libertariannews.org/ Michael Suede

            Math may be concrete but theories of bending space most certainly are not.

            Dark matter exists!  Oh wait, it doesn’t!  Oh wait, it does!  Does it exist?  Sounds real concrete to me.

          • J. Sharples

            Theories of bending space are part of mathematics – that’s what differential geometry is!

            Dark matter is a separate issue to the mathematical theory of general relativity

          • http://www.libertariannews.org/ Michael Suede

            Clearly.

            However, there is no proof that space actually bends.  In order for space to bend, it must have physical properties that can act upon matter.  There is no evidence such properties of space exist.  

            You may point to things such as the MM experiment, but if we look at LaFreniere’s work, we can see that there are alternative explanations for why such experiments turn up a null result other than bending space.

            Since bending “nothing” imparting force upon some “thing” is logically ridiculous, bending space should be rejected until all other possible avenues of physical explanations have been exhausted.

            http://glafreniere.com/matter.htm

            Physics must be tied to reality. Reality is clear that nothing can not impart force upon something.

          • Allanroser

            —–An iron curtain divides the subjects of gravity and electrodynamics, in today’s academically accepted versions of physics. Those attempting to cross it will risk the intellectual equivalent of machine-gun fire. Beyond, lie even more serious obstacles which come, not from outside, but from within the mind of the investigator. To get at the source of those self-imposed shackles, requires that we go beyond the bounds of what is today defined as “physics,” into matters usually classified as philosophical, or metaphysical. In doing so, we cannot avoid noticing that there are two schools in physical science, each one so distinct from from the other as to constitute two entirely different domains. It is the unfortunate aspect of our modern legacy that most, even among well-educated scientists, are unaware even of the existence of such a distinction. Yet, if the real history of physics of the 19th century were known, most of what passes as teaching of fundamental topics in that discipline today, would be shown to be, in the best of cases, misdirected, in the worst, willful fraud.—
             
             
            —The reader must be warned, at this point, against a probable misinterpretation of the import of statements made so far: That would be to assume, that, were my perfectly accurate historical statements to be proven valid to his satisfaction, it would only be necessary to correct some names and dates to make the accounts in existing textbooks more or less valid. The reader’s persisting error would involve, among other things, a confusion over our use of the term relativistic. From Kepler’s rejection of a reductionist treatment of the inverse square law of gravitation discovered by him, through the work of Leibniz, Huygens, and the Bernoullis on the common isochronic principle governing falling bodies and light propagation in an atmosphere, to Gauss’s devastating proof of Kepler’s planetary harmonics, in his discovery of the orbit of Ceres, there prevailed a conception of the foundation of physics entirely different from that taught in today’s respectable institutions of learning. Today, the term relativistic, means a formulaic correction to a system of equations and other formalisms premised on an assumed, self-evident notion of three-fold extension in space and one-fold in time. Up to, approximately, the 1881 seizure of power by Hermann von Helmholtz at Berlin University’s Physics Department, the leading minds of European continental science rejected such an underlying assumption as sophomoric.—
             
             
            —In the same memoir, Weber reviews the work of several astronomers, who attempted to apply his Fundamental Electrical Law to correct the law of gravitation, by including terms for the relative velocities and relative accelerations of a pair of bodies. One of the glaring anomalies in the Newton-Laplace theory of gravitation was its inability to accurately predict the advance of the perihelion of the planets, of which Mercury’s is the largest. (The phenomenon is famous as being one of the foundational proofs for general relativity.)
            In 1864, the Göttingen astronomer C. Seegers proposed to examine the advance of the perihelion from the standpoint that the gravitational force be represented in the same way as the Fundamental Electrical Law. Thus, the relative velocities and accelerations of the bodies of the solar system would have to be taken into account, and the factor 1/c2 introduced as a correction. Eight years later, Prof. Scheibner in Leipzig determined a secular variation of 6.73 arc-seconds for the perihelion of Mercury, attributable to the application of the Weber law. In 1872, Tisserand found the value 6.28 seconds for Mercury, and 1.32 seconds for Venus, by applying the Weber law.—
             
             
            —It is among the delightful ironies of the official cover-up known as modern scientific historiography, that the expression for the classical electron radius (a concept which is not supposed to come into existence for another 30 or more years), falls out of Weber’s expression—indeed, as a trivial case!
            It gets more interesting. Weber has already dared, in the 1870 paper, to conceive the notion we know today as the proton-electron mass ratio, which leads him to wonder as to the possible motions of the different configurations of particle pairs. It turns out that, according to his relativistic electrical law (one which was never considered in the accepted, modern formulations of atomic theory), it is possible to develop an orbital system for the case of a lighter electrical particle of one sign, orbiting a heavier particle of the opposite sign! It is also possible for two similar particles of the same sign to develop a closed system of oscillations along the straight line connecting them.—
             
            *http://www.21stcenturysciencetech.com/articles/spring01/Electrodynamics.html*

          • gooseass

            Hi Popil,
            Many thanks for your amusing comments!
            The debate here has amazed me that many “professional” scientists deal with theories without an ability to doubt aspects of them. When a theory becomes a religion, that’s when human wisdom fails. Max Planck said it all when he spoke of how a theory would change effectively over time.

          • Stephen J. Crothersmis

            Corda,

            First, you ignored my previous post and so I can only conclude that you are not interested in the facts, which does not surprise me. Second you misrepresent me because I have no knowledge of the theory of Prof. Myron Evans and the theory of Dr. A. Sharma. You further misrepresent me as to my expertise in differential geometry to which my previous post attests. You also falsely assert that I do not understand General Relativity again as my previous post attests. Third, you attack me ad hominen by calling me a crank instead of dealing with the facts in my previous post. Whether you like it or not the black hole is a dead duck, and was always a dead duck, and must surely find its place in the dustbin of scientific history. The paper you posted to the arXiv is nonsense, as my papers haven proven. Interested readers can find all my papers here:

            http://www.sjcrothers.plasmaresources.com/papers.html

            and on the vixra site.

            The waste of vast sums of public money in the search for black holes, Einstein’s gravitational waves and vestiges of the big bang nonsense must be stopped. The public purse has been fleeced by the peddlers of the foregoing nonsense.

            I refer you back to my previous post and request you to prove that my papers on differential geometry are wrong. This will be a tall order for you, because my referenced papers are valid.

            I see nothing wrong in posting our correspondence on scientific matters so that all interested in the subject can decide for themselves what is and what is not correct. You came off pretty badly in our correspondence and so you seek to prevent others from seeing this. I intend to ensure that our correspondence is made available to all interested persons.

            Stephen J. Crothers

          • Stephen J. Crothersmis

            The link in my last post should be

            http://www.sjcrothers.plasmaresources.com/papers.html

            Stephen J. Crothers

          • Stephen J. Crothers

            The Russian theoretician and specialist in General Relativity, Dr. Dmitri Rabounski, has confirmed that my analysis is correct that that black holes cannot form in Schwarzschild spacetime. Here is his straightforward paper:

            http://www.ptep-online.com/index_files/2008/PP-12-18.PDF

            The black hole, in all its forms, is nonsense.

            Stephen J. Crothers

          • orrery

            This Corda individual is all about ideology. There isn’t a single piece of scientific evidence to support the existence of Black Holes. Scientifically, it has no more merit than Time Machines, Worm Holes, Alternate Dimensions, or any host of flights of sci-fi fancy.

          • http://www.facebook.com/ralph.huntington Ralph Huntington

            “…but I use science, not ideology.”

            Excuse me, Dr Corda, with due respect, your replies suggest that more math than science has been employed in arriving at your conclusions. Your entrenched position very much resembles an ideology, even a religion, and you present as an adherent rather than an investigator. Your refusal to enter into related philosophical discussions surrounding the central topic further suggests the actions of an adherent, not a scientist. An investigator should welcome the question and the challenge, while someone with a vested interest in the status quo would not.

            Your blocking publication of a scientific paper based solely on your personal opinion further erodes your claim of being more scientific than ideological. Why not allow publication, if you are so confident in your theory, and let the scientific community decide what to believe? You could even publish a point-by-point rebuttal if you feel so strongly. Censorship is the tactic of an ideological adherent, not a scientist.

            Let me just say that from the perspective of this amateur scientist, black holes are charter members of a troupe of mythical, fanciful, imaginative, impossible ad-hoc band-aids slapped onto a medley of theories hopelessly falsified by observation and experimentation that comprise the Standard Model of Cosmology. The refusal of mainstream scientists to even allow challenges to their firmly held — I would say ‘cherished’ — beliefs, hints at a science community terrified by the prospect of Occam’s Razor slicing the Standard Model to ribbons.  With good cause, it would seem.

          • http://profiles.google.com/pskeptic Paranormal Skeptic

            Are you familiar with the peer review process?

            You can not allow publication of an article that isn’t right, and not even wrong.

            He needs to do what the Intelligent Design folk should have done:  Take the critique, and fix his theorem, then re-submit for publication.

          • gooseass

            Skeptic,
            Who decides someone’s paper is right or wrong? A small number of reviewers, or the test of time?
            How do you explain the recent incident involving an article in Nature by a Japanese geneticist and her colleagues (including a Harvard professor)? The authors are now accused of all sorts of things, including plagiarism, fabricated data, etc. etc. Although it is too early to tell the real nature of this incident, one should nevertheless ask: what really happened to Nature’s review process?
            Are you really familiar with the peer review process?

          • Paranormal Skeptic

            So, you’re not familiar with the peer review process either?

          • gooseass

            Of course, I am. Know too well about it from inside out.

          • Paranormal Skeptic

            So, you’re not familiar with the peer review process.

          • gooseass

            Hello,
            Don’t be kidding me. I’ve been on the editorial board of a first-class international journal (published by the Blackwell Publishing Co.) for the last 21 years.

          • Paranormal Skeptic

            Sure you have. If you actually were, then you would know about this thing called “rebuttals” to every peer-reviewed article…

            And, if you were, you would know there is no “right or wrong”, per se, in research. You publish your data, your methodology, and sometimes a conclusion. Which allows others to repeat your work. And, sometimes, people do repeat it, sometimes they find flaws in your methodology.

            So, when you asked,”Who decides what is right or wrong?”, if you were on a board of a peer-reviewed journal, you would have already known the answer: Repeat-ability, and failure to falsify the results when repeated.

            So, do you want to try and sell us another one “gooseass”?

          • gooseass

            Surely. But you have sidelined the point here and are only talking about general aspects of the review process, which everyone knows without ever being on an editorial board.

            The threads here are only about Mr. Crothers’s paper. Do you get the point? He wanted to publish his paper. Now where is the evidence that his paper was reviewed by peer referees? Where are the reviewers’ rebuttals? Did Mr. Crothers receive any? Any chance given to Mr. Crothers for his replies to the rebuttals?

            If you find the evidence from the debates and threads here, please point them to me.

            From your responses, I can tell that you have no real understanding of the peer review process and how it is used in academic journals. Most if not all journals treat submissions in a fair and rigorous manner. But sadly, sometimes the review process is abused by editors too, and based on my 20-plus-years of experience, I know that for a fact.

          • Paranormal Skeptic

            His paper didn’t get published because he’s not even wrong.

          • gooseass

            “You could even publish a point-by-point rebuttal if you feel so strongly. Censorship is the tactic of an ideological adherent, not a scientist.”
            Good point, 10thman. Instead of calling Mr. Crothers by names, Mr. Corda could (and should) publish Mr. Crothers’s paper together with a point-by-point reply by a reviewer. This is also a common process for academic debates when authors and reviewers both contend strongly and develop heated arguments about aspects of a theory and analysis.

          • brant callahan

            Because he is smarter than you?? Geniuses exist in various fields that have the ability to learn certain things much quicker than regular people… Ask me how I know….

          • New_Idiot

            Shut up you individualist.
            Everyone is a genius.

          • gooseass

            “I am not interested in philosophic discussions.”

            Really??? Ph.D. = Doctor of Philosophy

      • gooseass

        It seems Stephen Crothers is one of the few who can see that the emperor is naked.

    • http://profiles.google.com/pskeptic Paranormal Skeptic

      His papers aren’t even wrong.

    • Michael Wilson

      there is no such thing as a black hole, never was. a bunch of freaking liars all of you are!!!!

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • Raffyovr

    hurr durr I prove black holes arent really even though they are.

  • http://www.facebook.com/people/Brant-Ra/100001945176071 Brant Ra

    My math is not that great but even I can see the validity of the argument presented by Crothers.

  • http://profiles.google.com/fungusfitzjuggler Patrick Donnelly

    Well said!

  • Allanroser

    –. [I said that Mr. Crothers speaks idiocies, not that he is an idiot.]— Even intelligent people can speak idiocies sometimes.–   
    A quick browse through any of the main-stream Astro-physical publications/forums etc will prove beyond a doubt that Mr Corda’s statement is correct.

    • http://www.libertariannews.org/ Michael Suede

      “A quick browse through any of the main-stream Astro-physical publications/forums etc will prove beyond a doubt that Mr Corda’s statement is correct.”

      I concur.

      “I agree with you that black-holes do not exist” – Dr. Corda

      • J. Sharples

        Let’s be clear on one very important point: Crothers’ claims about the non-existence of black holes stem solely from his mathematical considerations. The points he attempts to make are not of a physical nature – except that he claims that the fact that BHs haven’t been observed (which is itself debatable) is proof that they don’t exist (does Mr Crothers also claim that atoms didn’t exist until they were observed?)

        So let us concentrate on the mathematics… the physical reality of BHs (or not) is not relevant.

        It is impossible to address all of Crothers’ shortcomings in a short post, so I will focus on two that have been mentioned in this thread:

        1. That r strictly plays the role of the inverse square root of the
        Gaussian curvature of the spherically symmetric geodesic surface in the
        spatial section of “Schwarzschild” spacetime and so does not itself
        denote any distance whatsoever in “Schwarzschild” spacetime.

        and

        2.
        There are no known solutions to Einstein’s field equations for two or
        more masses and no existence theorem by which it can be even asserted
        that his field equations contain latent solutions for multiple masses.

        In response to 1: the *coordinate function* r does not denote a distance in a spacetime. Nor does any coordinate function. A distance is given by an appropriate *integral* which maps a function into a scalar. The coordinate function r similarly does not strictly represent the inverse square root of the Gaussian curvature (scalar).  Crothers does not understand the concept of coordinate functions and so is unqualified to make serious inquiries into differential geometry, let alone GR.

        In response to 2: There certainly are known solutions to the Einstein equations for two or more masses. They are derived numerically. While these solutions are not given as closed-form analytic expressions, they are solutions nonetheless. In fact, if you check Crothers’ web page you will see that Stefan Gillessen patiently tried to explain this to Crothers to no avail. It is also wrong to claim that there are no existence theorems – there are: see the papers by Choquet-Bruhat and others. As an analolgy consider the Navier-Stokes equations for fluid flow, which also govern atmospheric circulations. In most cases of physical interest the fluid equations cannot be solved analytically and solutions must be obtained numerically – and yet weather still persists! The inability to find analytic solutions does not mean that no solutions exist.

        Another mathematical error that Crothers repeatedly makes is about Ric=0 implying empty space (and as such violating the conclusion that the spacetime contains a black hole). However, he fails to realise that the equation Ric=0 is only being considered over a region of spacetime that contains no matter, e.g. for the Schwarzschild case it is being considered outside a sphere, which the matter lies within. In this exterior region it is entirely valid to consider Ric=0. The effects of the matter inside the sphere are incorporated into the solution via the imposition of boundary conditions.

        • http://www.libertariannews.org/ Michael Suede

          For a better break down of the math that proves his point, see this video:

  • Allanroser

    To be clear I do not think Mr Crothers speaks idiocies, I left the statement in (but bracketed) so as not to take Mr Corda’s comment out of context.

    —Few people had shared Fessenden’s belief that broadcasting voices was possible. When he asked the opinion of a former employer, Thomas Edison, Edison replied, “Fezzie, what do you say are man’s chances of jumping over the moon? I think one is as likely as the other.—”

  • odobo

    I believe Mr. Crothers is experiencing the same type of response that Steve McIntyre is receiving for disputing the popular man made global warming theory (MMGW). I’m afraid Mr. Crothers will discover that no amount of truth, proof, or fact will sway people who are invested in a position when money, power or status is involved.

  • Sophistros

    Oh, good grief. This entire discussion is an object lesson in how adherents of alternative cosmologies block their ears to evidence disproving their chosen system, while spuriously citing the scientific method as reason for believing their own dogmas. Dr Corda’s perfectly reasonable interventions demonstrate that Mr Crothers’s assertions are disproved – the textbook ‘falsification’ of the scientific method – while his detractors display the blind faith that they purport to decry. As an impartial observer it is quite obvious to me who is being dogmatic, and who scientific. As more than one commenter has pointed out, Mr Crothers is functionally illiterate in the mathematics he is using to ‘prove’ his assertion. In summary, he makes no assertions about the physical world; instead, he makes a mathematical argument which is readily falsified. His argument is unsupported by any evidence, and thus his assertion cannot stand. This being the case, we must revert to the most mathematically complete picture of the Universe, and the one that most closely resembles observable reality, which is… GR.

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  • audiorago

    I understand that Crothers is a mathematician and does not hold a PhD in Physics. I have only a laypersons viewpoint but it seems that one would need to have an explanation of just what alternative Crothers can produce as per his math. Physicists create a formula to explain a hypothesis. They usually produce a paper explaining this which is then peer reviewed and then on to the experiment. Did Crothers ever explain what his math shows in regards to an alternative to the BB and GR? Has it been a peer reviewed paper? We already know that he has done no experiment where he can show any of this. Or did I miss this too?

    • http://www.libertariannews.org/ Michael Suede

      Crothers was in a doctoral program but was expelled for pursuing the truth.

      “My own experiences in academia for challenging “conventional wisdom” can be perused here. I was expelled from PhD candidature by the University of New South Wales. A professor of physics at UNSW (Professor Chris Hamer) even altered my work, and then claimed, on the basis of his alteration, that I was wrong.”

      http://www.sjcrothers.plasmaresources.com/PhD.html

      He has published several papers on this:

      http://www.sjcrothers.plasmaresources.com/

      http://www.sjcrothers.plasmaresources.com/papers.html

      It’s also worth noting that Crothers can falsify the existing theory without presenting an alternative. Having an alternative theory is not necessary before one can falsify an existing theory.

      • audiorago

        I agree but falsifying using only math without any explanation other than this integer or that representation of a particle or force is wrong or whatever mathematically. The only thing that this can say is that the math can be shown to have a weak link and that SC is absolved from showing what that really means physically. But remember that points in math as it relates to physics can be improved upon without dumping the entire theory. For example: Einstein’s Cosmological Constant.
        New data is compiled by real research scientists who have degrees in their fields who do the real falsifying by showing that it actually doesn’t work or voila it does. This data is then gone over by the scientists who came up with the math or refined the math and they either have to go back to the proverbial drawing board or – hey – they were right and their predictions are born out. What SC does is only the very first part – he sees formula – goes through many calculations and comes up with a potential problem with the math. Fine – he may show that the math has problems – but one can not argue that technology has come out of these theories which have given us the transistor and GPS. If the explanations don’t work – then how does the technology? SC doesn’t “have” to explain it – but if he wants to be considered anything other than a mathematician – then he will go further than just equations. I may be wrong here – but as a layman – I don’t appreciate a page full of equations without an explanation. That was the beauty of Feynman. He saw that many people even physics students had problems with fully understanding physics only through equations and created his famous diagrams which explain the math. SC doesn’t even provide a diagram to show an alternative. Nothing – just equations.

  • audiorago

    Again, I could be off base here but it seems that the EU folks show disagreement in the explanations of the math of GR while knowing little or nothing of the math while Crothers and his followers take issue with the math, knowing at least a fair amount of it while understanding little of how to explain the reality from their own math nevertheless the math of GR. Am I wrong here.