Event Horizon and Light Exit Cone Question

[noblackhole]

As I had already mentioned in this thread, Stephen J Crothers (who presumably either owns or is connected with the user name noblackhole) is so ready to find fault with so many things that this makes it very difficult to accept anything he says. If I hadn't already agreed with one of the things he said, I'd probably have dismissed him immediately as a crackpot.

For the original point about the Schwarzschild radial coordinate, he makes some very useful mathematical contributions, and I've found his generalization of the radial coordinate very interesting. However, he also claims to find fault with many other aspects of GR and makes some blanket statements which seem very silly to me (for example that SR "doesn't allow infinite energy density"). Although there may be some truth somewhere in these other statements, his readiness to find fault means that I will not be able to accept them unless I can absolutely follow all the logic (especially the hidden assumptions) and prove them to my own satisfaction.

I will however commend him on being open to at least some suggestions, in that he previously insisted on rewriting the term "Euclidean" using a different spelling based on a phonetic spelling of how the equivalent name would be pronounced in modern Greek, but in this latest paper he is now using the traditional spelling.

It is of course very difficult to argue rationally against the establishment position without sounding like a crackpot, but I think that even if Stephen Crothers is right he is going to have a hard time persuading the people that matter with his confrontational approach.

Crothers did not say anywhere that "SR doesn't allow infinite energy density". He clearly said and proved by simple algebra that SR forbids infinite density, because infinite density implies infinite energy or equivalently that a material body can acquire the speed of light in vacuo. This is in the cited article.

 

[Jonathan Scott]

Crothers did not say anywhere that "SR doesn't allow infinite energy density". He clearly said and proved by simple algebra that SR forbids infinite density, because infinite density implies infinite energy or equivalently that a material body can acquire the speed of light in vacuo. This is in the cited article.

Perhaps I shouldn't have written that in quotes as in the latest paper it wasn't exactly those words, but the statement that "SR forbids infinite density" seems to me to have exactly the same meaning as "SR doesn't allow infinite energy density".

The statement "infinite density implies infinite energy" on its own is extremely naive. SR is perfectly capable of describing a point-like finite mass, which has infinite density. This is like a Dirac delta function (the derivative of a step function). It is outside the scope of SR to describe how such an object could be created, but I'm not aware of any problem with describing how it behaves in SR. It is obviously not possible to achieve infinite density by accelerating a material body, but no-one was suggesting that this method would be used.

As far as I'm concerned, this particular point (and hence section 2 of the article) appears to be completely spurious, and therefore actually undermines the rest of Crothers' argument somewhat, but in any case it seems irrelevant to the specific arguments about the Schwarzschild radial coordinate.

As should already be clear, I find Karl Schwarzschild's original interpretation of the radial coordinate far more plausible than the black hole interpretation. However, that doesn't constitute proof. There is some experimental evidence (relating to the lack of Type I X-ray bursts) which appears to support the idea that neutron stars turn into black holes at some mass threshold, and there is also some experimental evidence (relating to intrinsic magnetic fields and radio-loud quasars) which suggests that supermassive bodies are not in fact black holes.

I don't really care whether Crothers, Mitra, Antoci and others have made mistakes; everyone makes mistakes sometimes. If they do it too often, or the mistakes are too blatant, then that obviously undermines credibility, but that doesn't prove that everything they say can safely be ignored.

As I've said before, what I would really like to hear is a clear rationale from the black hole supporters as to why they use Hilbert's assumptions about the radial coordinate when Schwarzschild's original model is more physically plausible. The mere fact that one CAN (in that there is a coordinate system which gets past the origin) does not seem to me to be a sufficient justification.

 

[atyy]

As I've said before, what I would really like to hear is a clear rationale from the black hole supporters as to why they use Hilbert's assumptions about the radial coordinate when Schwarzschild's original model is more physically plausible.

OK, let's see if I can convey some of Hawking and Ellis without garbling it too much. The two "interpretations" differ only by a coordinate change, so they cannot be different. But in any case, no one uses the interpretation of the Schwarzschild radial coordinate R=0 as the centre of the central mass. Also, the interpretation of the Schwarzschild mass parameter M_o as a Newtonian mass is irrelevant.

The mere fact that one CAN (in that there is a coordinate system which gets past the origin) does not seem to me to be a sufficient justification.

Yes, just because the maximally extended solution exists theoretically doesn't mean it exists in nature. But Birkhoff's theorem states that it is the maximally extended Schwarzschild solution that has to be used outside a spherically symmetric star, so we know that it is the extended coodinate system that is relevant for stars, which we do know exist in nature. The theorem itself doesn't say that we have to use the Schwarzschild part or the extended part, so there is no interpretation yet.

We start with the solution for the interior of the star, with some mass function m(Ri), the interior radial coordinate. Then we figure out where the surface of the star is Ri=Rs (Rs is the stellar surface, not the Schwarzschild radius). This determines which part of the extended Schwarzschild solution we need to use - we need to use it for Schwarzschild coordinate R>Rs - this is the where interpretation of the extended Schwarzschild solution first enters. The interpretation of the Schwarzschild mass parameter is done by setting M_o=m(Rs). Notably, this is not the mass (determined number of atoms, neutrons or other particles) of the star. So it is the interior solution (completely normal physics) which determines the interpretation of the extended Schwarzschild solution.

Then by considering stellar dynamics, it appears that for some stars late in their evolution we need to match to the extended part of the extended Schwarzschild solution. The matching is still determined by the normal physics interior solution, and we are only using part of the extended part of the extended Schwarzschild solution, and there's no singularity. Remarkably, there are a couple of theorems that say that if the normal physics interior solution requires us to match in the extended part, the star cannot be stable, and will collapse until ...? Either a black hole or General Relativity is wrong - the latter could be the case, but I think the usual interpretation of the possibly wrong theory is correct.

So apart from Birkhoff's theorem, Hawking and Ellis rely heavily on theorems that there are no stable normal physics interior solutions if the normal physics interior solution is matched to the extended part of the extended Schwarzschild solution, and that within the framework of General relativity, a singularity is inevitable. These theorems apparently fail if conditions are not sufficiently symmetric, and they are careful to state that.

Also, the M/Ri ~ 2 (M is not the Schwarzschid mass parameter M_o) that I made fun of is actually due to carefulness, because the interior coordinate Ri has different interpretations depending on the density and pressure profile of the star.

I might be totally garbling this, but you should look at Hawking and Ellis, because they really distinguish between all the different mass-like terms, and radius-like terms under consideration, and also talk about effects of temperature and other uncertainties. In short, they seem to have been very careful.

 

[Jonathan Scott]

OK, let's see if I can convey some of Hawking and Ellis without garbling it too much. The two "interpretations" differ only by a coordinate change, so they cannot be different. But in any case, no one uses the interpretation of the Schwarzschild radial coordinate R=0 as the centre of the central mass. Also, the interpretation of the Schwarzschild mass parameter M_o as a Newtonian mass is irrelevant.

I wouldn't say "cannot be different". Outside the radial coordinate of the "event horizon", the interpretation makes no difference to the physics. The physical difference is in the location of the point mass for that hypothetical case, or in the way in which an interior solution for the central mass is joined to the vacuum solution, where the assumption is in the way the radial coordinate for the central mass is assumed to go over into the Schwarzschild radial coordinate (as interpreted by Hilbert), or into some other radial coordinate.

Yes, just because the maximally extended solution exists theoretically doesn't mean it exists in nature. But Birkhoff's theorem states that it is the maximally extended Schwarzschild solution that has to be used outside a spherically symmetric star, so we know that it is the extended coodinate system that is relevant for stars, which we do know exist in nature. The theorem itself doesn't say that we have to use the Schwarzschild part or the extended part, so there is no interpretation yet.

To put it another way, Birkhoff's theorem says that any solution must be a subset of the maximally extended Schwarzschild solution, but this must not be taken to imply that there is necessarily any case where where the part of the solution inside the event horizon applies.

We start with the solution for the interior of the star, with some mass function m(Ri), the interior radial coordinate. Then we figure out where the surface of the star is Ri=Rs (Rs is the stellar surface, not the Schwarzschild radius). This determines which part of the extended Schwarzschild solution we need to use - we need to use it for Schwarzschild coordinate R>Rs - this is the where interpretation of the extended Schwarzschild solution first enters. The interpretation of the Schwarzschild mass parameter is done by setting M_o=m(Rs). Notably, this is not the mass (determined number of atoms, neutrons or other particles) of the star. So it is the interior solution (completely normal physics) which determines the interpretation of the extended Schwarzschild solution.

Yes, I think the implicit assumption about the radial parameter occurs when matching up the radial coordinate for the inner boundary of the vacuum solution with the radial coordinate for the outer boundary of the interior solution. Any specific assumption about how these coordinates join up (given that they are parts of different solutions) has physical implications.