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Re: Singularity Temperature



Regarding Glenn A. Carlson's comment:

But I assert that the temperature of matter inside the black hole (though
not at the singularity) is just as real and no different that the
temperature of matter outside the black hole. The temperature of matter
inside a black hole is only unobservable from outside the black hole. If
you are inside a black hole, you can measure the temperature of infalling
matter in just the same way as if you were outside the black hole. You
just wouldn't be able to communicate your measurement to anyone outside the
black hole.

I mostly agree with this. But I want to point out that the concept of
the matter inside the event horizon as being characterized as "infalling"
is misleading. An observer *outside* the horizon *does* understand any
matter falling through the horizon (even if it may take an infinite time
for it to *appear* to do so) to be legitimately called 'infalling'.

But once the matter is inside the event horizon it is *not* falling
through space in time toward a central singularity in space. Rather, the
matter finds itself in a region of spacetime where the space itself is
contracting. The singularity is *not* a point in *space* (nor is it a
point missing from *space* where the local curvature happens to be
infinite). Rather, it is a point in *time*--actually its a region
removed from spacetime that happens to be in the finite *future* of *all*
possible observers inside the horizon (assuming for now that the hole is
non-rotating) where the local curvature is diverging. The matter inside
the hole becomes more dense as the space it is in locally contracts sort
of like a mini-version of a Big Crunch which occurs *everywhere* inside
the hole at some point in the future of the matter there. One *big*
important difference between a Schwarzschild singularity and a
cosmological Big Crunch singularity is that the former has the
contraction of all space in the universe taking place *isotropically*;
whereas inside the hole this contraction is very *an*isotropic for only
the region interior to the horizon. In fact, it is *so* anisotropic that
space is really only contracting at all in just 2 of the 3 spatial
dimensions, and is actually rapidly *stretching* in the 3rd dimension.
But the overall volume of any appropriate tiny volume element is,
nevertheless, inexorably contracting anyway. The singularity occurs when
the space has been infinitely compressed in 2 dimensions and infinitely
stretched in the 3rd. Obviously, such behavior plays havoc with any
object that is supposed to be an extended solid body. These tidal forces
will shred up any such body into a long very thin stringy shape before it
is completely destroyed at the singularity in its future.

(BTW, for a rotating black hole things can get much more complicated than
this inside the event horizon.)

David Bowman
David_Bowman@georgetowncollege.edu