Re: black hole and special relativity

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Glenn Carlson's question:

> > It is possible to prove a
> > theorem that says that if a spherically symmetric object is stable
> > against gravitational collapse then its radius *must* be strictly greater
> > than 9/8 of the Schwarszchild radius for that mass if it was collapsed to
> > a (Schwarszchild) black hole.
>
> I'm intrigued.  Do you have a reference for this theorem?

I just got a chance to look it up in Weinberg's
_Gravitation_and_Cosmology_.  See chapter 11, section 6 pp 330-335.

Also MTW, in section 23.7, Box 23.2, pp 609-611 show this result for a
model star of uniform density, but they don't seem to make the necessary
connection that such a model is the limiting case for any more realistic
spherically symmetric mass distribution (like Weinberg does).  IOW, for
any realistic (spherically symmetric) static distribution of mass that
is non-uniform, the value of the ratio of its radius to its Schwarzschild
radius at the point where the central pressure diverges to infinity is
*at least* (the uniform mass distribution value of) 9/8 (and only equals
this value when the mass distribution really is uniform).

David Bowman
David_Bowman@georgetowncollege.edu