Op zaterdag 16 april 2016 08:38:51 UTC+2 schreef Steven Carlip:
First, in classical general relativity the
horizon is empty space -- there's nothing material there.
Second, for a large black hole, the curvature at the horizon
is very small.

Snip

You can *calculate* Hawking radiation, using what are now
standard methods of quantum field theory in a curved background.
The result is definitely not a pure state.

Again, it could be that this calculation is badly wrong. But,
again, the problem is to explain *why* it's wrong.

The first thing is to verify why your calculation is correct.
For example you have to very that the BH "emits" radiation.
and that the predicted energy range is correct.

That's not clear. if in-falling information just bounces back
at the horizon then that's local (as could happen in the
eternal equilibrium hole).

That makes no sense. There's nothing *at* the horizon. It's
just empty space. It's true that "new" matter falling in can
interact with Hawking radiation coming out -- this is something
't Hooft has been working on lately -- but I don't see how it's
relevant to the setting in which the paradox is posed, which is
a black hole forming from collapse of a pure state and then
evaporating.

Gerard 't Hooft at page 43/44 of this document:
http://www.staff.science.uu.nl/~hoof...cturenotes.pdf
discusses the same issue.
IMO the evolution of a BH is a very complex lengthy process.
When you consider the sketch of a BH in:
https://astronomynow.com/2016/03/11/...ve-black-hole/
the center is completely black i.e. empty.
The question is if that is true. I doubt that.
One question is: if there is empty space around a BH.
At page 29 G'tH writes:
" Thus, as soon as matter falls in, the marginally trapped surface
is replaced by a larger one. We can therefore conclude that
the area of the horizon increases when matter falls in."
Which implies that the region is not empty.
At page 42/43 G'tH writes:
"According to Hawking's derivation of the radiation process,
any black hole, regardless its past, ends up as a thermodynamically
mixed state. Would this also hold for a black hole that started
out as a collapsing star in a quantum mechanically pure state?
Can pure states evolve into mixed states? Not according to conventional
quantum mechanics."
Immediate next he writes:
"From a physical point of view, the distinction between pure states
and mixed states for macroscopic objects is pointless.
Black holes should be regarded as being macroscopic."
I agree with this last sentence. In a sense it removes the problem
what pure and mixed states are.

That is why I wrote in a previous posting:
The problem is much more a physical, chemical problem.
At the same time it is also an information problem in the sense that
we cannot directly observe a BH. That means it is extremely difficult
to observe that the life cycle time of a BH is finite.
It is a murder without a body. For a star this is much simpler.

Nicolaas Vroom