Re: On the controversy about the Schwarzschild radius and black holes
- From: Ben Rudiak-Gould <br276deleteme@xxxxxxxxx>
- Date: Thu, 18 Jan 2007 09:33:36 +0000
cafeinst@xxxxxxx wrote:
I think the best way to understand the controversy is to
read the paper: arXiv:physics/0002009. One can also read other papers
by Crothers here http://www.geocities.com/theometria/ but I think
Brillouin's is the best by far, since it is short and to the point
and also illustrates the majority opinion in 1923, that black holes do
not exist.
I feel like we're going in circles. In the last thread I made the following claims:
1. The observable behavior of black holes depends only on the exterior
geometry.
2. None of the authors you've quoted disagree with each other or the
mainstream on what the exterior geometry is, or on its reality.
3. The exterior geometry can be extended, mathematically, to an
interior region.
4. You're free to believe anything you like about the reality of the
interior region. Respectable physicists can and do have different
opinions about this.
Do you disagree with any of this? If so, which part and why?
The current majority point of view that black holes exist is based on
the view that coordinates in space-time do not matter - coordinates are
human inventions and can be massaged by humans legitimately.
No, the majority view that black holes exist is based on the existence of astronomical observations that match the predictions of the black hole model and don't match the predictions of any other model that anyone's come up with. The only way to convince people that black holes don't exist is to come up with another viable model of what's seen. Claiming that there's some sort of theoretical problem with the current model isn't going to help, because, for one thing, none of the authors you've quoted in your defense actually disagree with the part of the black hole model that's being used to make these predictions.
The statement that coordinates are human inventions is a red herring. It's true in general relativity. It's true in Newtonian mechanics. It's true in plane geometry. Or it's false in all of them, depending on what you mean by it.
[...] Einstein's General
Theory of Relativity is based on the assumption that space-time is
*space-time* and not Kruskal-Szekeres time. In order for the
mathematical entity, space-time, to be space-time, it is necessary to
be able to label all of the coordinates with three distance dimensions
and one time dimension in which when the distance from the center of
mass becomes arbitrarily large, the space-time metric becomes
Minkowski.
You're trying to come up with a philosophical standpoint from which it follows that the black holes that you don't like don't exist. But I can't even understand your philosophy, and I wouldn't have any reason to accept it if I did. Even you don't accept it for any reason but that it leads to the conclusion that you want. I'm willing to concede that spacetime should be (and indeed is) spacetime. Beyond that nothing that you've said here makes sense to me.
Maybe (this is kind of a stab in the dark) you might be interested in the tetrad formulation of general relativity, which is an alternative to the metric tensor that enforces that spacetime is 3+1 everywhere. E.g. the metric tensor g_uv = diag(1,1,1,1) doesn't have a tetrad equivalent. But the Kruskal-Szekeres geometry can be expressed with tetrads, so this doesn't really help your case.
Clearly, with respect to black holes, this is not the case,
as whenever you go past the event horizon of a black hole, time becomes
space-like and space becomes time-like.
It's meaningless to say that time becomes spacelike (or vice versa). Time is timelike by definition.
Again, the exterior solution can't be extended past r=2M, because Schwarzschild coordinates are not valid at r=2M. In particular, r=2M in schwarzschild coordinates is not the event horizon.
Furthermore, crazy stuff like
the limit of the ratio between the circumference and the radius
approaching infinity at the event horizon and t=infinity should not
happen in a real space-time.
What radius? You mean the radius that's defined to approach 0 at the event horizon? Obviously, then, the ratio is going to blow up. I can choose coordinates for plane geometry which make the same ratio blow up.
In any case, the spacetime you're arguing here doesn't exist is a spacetime that all of the authors you've quoted believe does exist.
-- Ben
.
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