Jonathan Scott
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JustinLevy said:We don't need to argue by authority here. This is simple enough we can solve ourselves.
Do you, or do you not, agree that the integration constants from the vacuum solution are uniquely fixed by:
1) the boundary condition at infinity
and
2) the source term
?
This is not rhetorical. Please answer this question.
In a sense, what is affected is a third term, the origin.
The published papers by Salvatore Antoci (available in copy on the ArXiv) specifically address this point. A translation of the Schwarzschild original paper can be found at arXiv:physics/9905030v1 and an excerpt of Hilbert's paper where he changed the assumption can be found in Antoci's later paper: arXiv:physics/0310104v1
The difference does not affect the results outside the Schwarzschild horizon but simply whether one can reach it or not.
Antoci is not saying that Hilbert's assumption is necessarily wrong, but rather that Hilbert made a different mathematical assumption from Schwarzschild that has different physical consequences, in particular making black holes possible, and that there doesn't seem to be any theoretical way at present to prove either assumption correct or incorrect, but Schwarzschild's original idea avoids the problems of black holes even if it's mathematically less general.
I have tried to understand the detail myself, in particular Schwarzschild's original paper and what his model implies.
In the various arguments I've seen, those supporting Schwarzschild's original assumption do not have any obvious faults as far as I could see, and I've followed those up by doing my own modelling (including my conceptual picture of replacing the point mass with a hollow sphere in the standard solution and poking a ruler through it) to look for inconsistencies, which so far I've not found, but this is obviously not a well-researched area and there could well be problems I've missed (which is what I'm hoping to expose through discussion).
I'm also obviously satisfied that Hilbert's version (as in standard GR) is self-consistent too.
However, it seems to be near-impossible for anyone who has "grown up" with Hilbert's version to see the alternative picture and provide any constructive criticism of it. The arguments they present usually seem to be circular, based on assuming some aspects of Hilbert's position. I've also seen some really quite nasty attacks of the form "if you don't understand why Hilbert was right to correct Schwarzschild, you must be stupid", but this doesn't help me understand anything.
Personally, I feel that if I'm expected to accept the weirdness of black hole theory, I need to understand why in a way which really convinces me, which I'm not getting, and given that there appears to be an alternative which is still consistent with Einstein's field equations, I want to know why I should choose one over the other. (I accept weirdness when there's strong enough evidence for it, as with Bell's inequality and entanglement, but I don't like just being expected to take someone's word for it).