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Old April 22nd 16, 03:54 AM posted to sci.astro.research
Jos Bergervoet
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Posts: 126
Default Paradox unexplained

On 4/16/2016 8:38 AM, Steven Carlip wrote:
There are a couple of things to keep in mind when discussing
this problem. 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. That means that, by the equivalence principle,
a freely falling (classical) observer will notice nothing
special happening as she crosses the horizon.


This of course makes it likely that the whole firewall idea
was meant as a provocation. (The intended message may have
been "Compared to the other alternatives this is still the
most likely one, so imagine how bad things are!")

The consistent
problem with many proposed "solutions" to the information
loss paradox is that they require drastic changes in the
physics in these empty, low curvature regions that are, at
least classically, locally indistinguishable from anywhere
else.


But some of those solutions might perhaps still work if the
"firewall" exists not exactly at the Schwarzschild radius
(since indeed there is nothing special there.) The
supertranslations, for instance, are probably everywhere in
space. (But that was a question I already asked in a separate
thread, since the topic here is about the precise definition
of the problem and the supertranslations are, or at least
taste like, some solution!)

....
Well, we can certainly write a classical solution in which
matter collapses to form a black hole. We can also make
this "semiclassical" -- that is, we can write down a quantum
state describing, say, a thin shell of radiation and use
the expectation value of its stress-energy tensor as a source.


You then start with the Vaidya model, I presume (as the Hawking-
Perry-Strominger paper in their first example). But we should
use the quantum-mechanical amplitude distribution of the fields
that are the source (as opposed to merely expectation values)
and thus arrive at a quantum-gravity description..

Now, it *could* be that if we could somehow carry out this
same analysis in a completely quantum mechanical setting, the
results might be completely different.


Something like the Mermin-Wagner 2D instability could perhaps
create a "firewall" after all! But I don't see how anything
special exactly on the Schwarzschild radius could be explained.
(Surely Polchinski must be joking, I still think.)

...
Such a black hole will then evaporate
by Hawking radiation, which is thermal.


This again is not so clear, as the Polchinsky-paper
http://arxiv.org/abs/1207.3123
states immediately in the abstract: we want it to be a pure
state! You are now claiming something that is not granted.


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.


The basic definition of quantum field theory is a quantized
string which is in a pure state. (Weinberg vol. 1, Sect. 1.2,
"The birth of quantum field theory.") If you calculate merely
expectation values you don't calculate the actual time-
evolution of the actual quantum field.

..
This almost certainly means that "late" Hawking radiation,
emitted near the end of evaporation, must be correlated with
much "earlier" Hawking radiation.


Of course. And a deterministic time evolution guarantees that
all Hawking radiation in the end is exactly correlated to the
initial pure state, so there is no problem. (Unless we mess
with the unitarity, but why would we?) Our only problem is to
seek out the path of the information flow without non-local
jumps. It's a topological problem.

But late Hawking quanta
are never in causal contact with early quanta.


They certainly are, since QFT is causal. No quanta will
be created unless at the same event others are annihilated.
There is an unbroken chain of events. That is what the terms
in the Lagrangian do in a *local* quantum field theory. And
our standard model is a local QFT.

.. So this would
seem to require some highly nonlocal interactions. This would
mean a breakdown of the effective field theory description,


If the supertranslations effectively make a copy of passing
early quanta then the information is available. The no-cloning
theorem might not apply (like in a CNOT gate) if they just
entangle the information (with a pure gauge, or zero photon,
whatever) which *still* is deterministic, unitary time-evolution.

again in a place where curvatures are small and there's no
evident reason for the description to break down.


As the Hawking paper says, it's not yet an exact explanation
of how the information flow works (in any case the paper does
not attempt to depict the exact flow) but it opens some new
possibilities.

....
For that, we clearly cannot use the static Schwarzschild
solution, and just using Kruskal-Szekeres coordinates won't
help since they still describe the same solution. Is there
any closed form solution for the "transient black hole"?


There are many proposals. We have no idea which, if any,
of them is correct.


The Penrose diagram of the causal structure of the transient
black hole, as I understand it, is like this:
http://i.stack.imgur.com/Qtjrx.png
But in Hawking-Perry-Strominger Fig. 2 they have another which
looks more weird. Whereas their Fig. 1 (for the Vaidya model)
seems normal. I also have nothing against there time split and
"turn-on" of evaporation. What I don't understand in Fig. 2:

1)Why is the singularity not shown? It exists in a seperate
region of the manifold in http://i.stack.imgur.com/Qtjrx.png
but Hawking et al. seem to ignore its presence.

2) Why are there curved corners in the inner square? If that's
the horizon, it should be light-like and keep its diagonal
direction until its 2-sphere size vanishes (but then the
evaporation would be finished, which is not what the drawing
suggests).

...
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.


OK, there can't be a firewall or anything special there, so
if we assume that matter falling in will be locked in a remnant
but information about it remains outside, it's solved.

So what was wrong with just accepting a remnant disjunct from our
universe? You still can have Hawking radiation. You still can
have the infalling matter encoding pure-state Hawking radiation.
It's all about keeping some information outside.

What Fig. 2 in the paper seems to suggest that *not only* the
information paradox is solved, but also the remnant is non-
existent! I feel like I could (given some time) understand the
former, but not the latter. What am I missing? (Yes, lots of
things, probably. :-) )

--
Jos