Singularity Temperature

[Ben Crowell <crowell01@LIGHTANDMATTER.COM>]

Hmmm...the thermodynamics of black holes is the train of thought
that started Hawking on the path to figuring out black
hole evaporation.

Jack Uretsky wrote:
> In any event, matters inside the black hole's event horizon are
> not observable, so I'm not sure that your question has meaning.  If I
> were to answer your question "yes" there is no possible experiment that
> could falsify my answer.
Well, there are a lot of objections I'd make to this argument:
(1) There are such experiments, but if I do them, I just won't be able
to get them published in Physical Review.
(2) We can still calculate things inside a black hole using the
known laws of physics.
(3) The beauty of black hole evaporation is that thermodynamics
/doesn't/ break down, and quantities like energy and entropy don't
just get swept under the rug and eliminated by putting them in
a black hole. All the entropy comes back in the form of
radiation. All the energy is still there, and produces observable
effects (gravitational fields) elsewhere in the universe.

Jack Uretsky wrote:
> The meaning of <at the singularity> is still not understood.
> It awaits, in approximately the language of Misner, Thorne and Wheeler,
> the consummation of the wedding between quantum mechanics and general
> relativity.
Just because there is no general theory that unites quantum
mechanics and general relativity, that doesn't mean nothing
can be calculated or discussed that involves both theories.
Black hole evaporation is one example. You just have to expect
confusion and contradiction now and then, like when Bohr
was first working on the early quantum theory.

Tim O'Donnell  wrote:
> My thinking is that it maybe absolute zero,
> because just about everything that can be squeezed out is
> probably long gone.
Since Hawking showed the entropy eventually comes back out,
it seems to me that the temperature can't go to zero.
At zero temperature, there's wouldn't be any entropy.

Naively, I'd expect the temperature to get very high near the
singularity, assuming that any matter at all is falling in.
This just seems reasonable by analogy with white dwarfs and
neutron stars. You release a lot of gravitational potential
energy when matter falls into a deep gravitational potential.

Trying to be a little less naive, I'll throw out a few ideas:
(1) The answer may depend on your frame of reference.
(2) The answer may depend on the detailed dynamics of what's
happening inside the black hole. The theorem that a black hole
has no hair only applies to the /outside/, right?
(3) It seems logically possible that both the singularity and
the rest of the space inside the event horizon carry macroscopic
fractions of the heat and entropy, but it also seems logically
possible that one or the other gets no macroscopic share at all.
(4) The subject line of the original post referred to
singularities, not black holes. I wonder if the answers
might be different for naked singularities, if they exist.