Re: On spherical gravitational collapse and the stability of classical black holes.

On Jul 3, 3:44 pm, Bilge <dubi...@xxxxxxxxxxxxxxx> wrote:
On 2007-07-01, LEJ Brouwer <intuitioni...@xxxxxxxxx> wrote:

Because the interior solution of the Schwarzschild black hole does not
have such a spatial spherical symmetry (it has an SO(3) symmetry where
the radial direction is timelike - i.e. a temporal rather than a
spatial spherical symmetry), this means that the matter responsible
for the formation of the black hole is NOT part of the black hole
interior (i.e. the Schwarzschild interior), even though it was

I have no idea why you aren't able to get the point here.

(1) The interior and exterior schwarzschild coordinates describe
the interior and exterior of the black hole, respectively.
They can't be joined across the horizon, so your attempt to
interpret the interior solution as if it extended across the
horizon so you can match up the labels, is fallacious reasoning.

(2) If you want to compare the geometry on the inside to the geometry
on the outside, precisely why do you object to using any coordinate
system which is actually valid in the region containing both points?
Performance art? A desire to be different for no particular reason?

[...]

To conclude, the standard picture of spherical gravitational collapse,
which assumes that infalling matter crossing the event horizon
contributes to an increase of the mass of the black hole, is incorrect
on mathematical grounds as the symmetry of the matter responsible for
the formation of the black hole is incompatible with the symmetry of
the Schwarzschild interior, so that the two regions must in fact be
distinct.

I find it rather bizarre that you consider any coordinate system that
is valid through the horizon to be invalid for the purpose of comparing
the geometry on either side of the horizon. So, are you saying that to
make a valid comparison, one must choose two coordinaate systems for
which there exists no valid means to join them?

I am not talking about sewing together coordinate patches here. That
was the subject of an earlier (and quite different) discussion.

.

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