[Moderator's note:  My apologies for the delay; this post ended up in
the wrong email folder for some reason.  -P.H.]

On 6/1/12 6/1/12 - 2:08 AM, Anon E. Mouse wrote:

Hmmm. In GR, a Schwarzschild black hole contains no matter. It is simply
a configuration of the fields (metric) that is static and satisfies the
field equation with reasonable boundary conditions. Energy-momentum
conservation is satisfied throughout the manifold (including inside the
horizon).

If one adds an infalling spherically symmetric mass shell to Schw.
spacetime, then the shell intersects the singularity in finite proper
time, and once it intersects the singularity the manifold is isometric
to a higher-M Schw. manifold [#]. For a solar-mass black hole, the
proper time between crossing the horizon and intersecting the
singularity is on the order of a microsecond.

        [#] Speaking loosely; this is difficult to specify precisely.

This Higgs boson in the standard model of particle physics is COMPLETELY
DIFFERENT.

Hmmm. You are confused, or at least using words funny. The Schwarzschild
and Kerr manifolds have T=0 everywhere, including inside the horizon of
the black hole. That is, they have no mass/energy ANYWHERE.

Manifolds with a black hole and infalling matter have T!=0 for a while,
but ultimately they also have T=0 everywhere [#], with the exception of
an EM field in the case of a black hole with net charge -- in general
that is VASTLY smaller than the "mass" one would assign to the black
hole from distant measurements of its gravitation.

Note that it is not clear that one can describe the singularity as
"inside" the black hole, as it is not part of the manifold and such
relationships only apply to the manifold. Colloquially we say that it is
"inside the black hole", but this is certainly loosely stated and has
problems when analyzed closely.

        Consider the limit points of all geodesics intersecting the
        singularity of Schw. spacetime. They are certainly inside the
        horizon. But the singularity is not its limit points....

Not so. The field equation applies, and it permits the gravitation of a
black hole to persist even though it "contains" no mass/energy (same
caveat as for "inside" above).

WHERE????? Having a location implies it is localizable in the manifold,
but it isn't.

Bottom line: black holes are WEIRD, and common language is inappropriate
for them. Because, of course, that language evolved without knowledge of
them. Beware of colloquialisms that don't actually reflect the math or
actual structure of the manifold.

Not GR. In GR the metric of a vacuum manifold can have a configuration
with gravitation, such as Schw. and Kerr.

Non sequitur.

You are ignoring boundary conditions. Every differential equation
requires them, and the field equation is no exception. The "stuff" you
seem to think is "missing" is actually outside the boundary of the
manifold. Yes, that is "missing" in some sense, but not in all senses.
Once boundary conditions are included (as they must be), I see no issue
with the "completeness of the EFE".

This does not apply to GR.

No. Inside the horizon of a Schw. black hole, no timelike or null
trajectory ever goes to higher "radius" (in the sense of closer to the
horizon or further from the limit points of the singularity). I'm pretty
sure that similar conditions apply to all black-hole manifolds.

Stated differently: every spherical surface inside the horizon is a
closed trapped surface; the horizon is merely the outermost one.

Tom Roberts