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Here is a paper that sets out a coherent view on black hole entropy including embracing the nonunitary effective dynamics of the exterior region because it provides an explanation of why the generalised second law holds: Ten Theses on Black Hole Entropy by Rafael Sorkin. (edit by F. Dowker)

From Ted Jacobson: Here are a few references relevant to BH information that I mentioned in my overview.

Bekenstein introduces concept of BH entropy:
"Black Holes and Entropy"
http://adsabs.harvard.edu/abs/1973PhRvD...7.2333B

Banks-Peskin-Susskind disaster (Markovian pure to mixed evolution violates locality or energy-momentum conservation):
"Difficulties for the evolution of pure states into mixed states"
http://adsabs.harvard.edu/abs/1984NuPhB.244..125B

Unruh-Wald rejoinder (energy-momentum conservation violation can be sequestered to act only on states that are not normally observed;
also, non-Markovian evolution can avoid all problems)
"Evolution laws taking pure states to mixed states in quantum field theory"
http://adsabs.harvard.edu/abs/1995PhRvD..52.2176U

Wilczek: the nature of correlations needed to maintain purity illustrated in an accelerating mirror model:
"Quantum Purity at a Small Price: Easing a Black Hole Paradox"
http://adsabs.harvard.edu/abs/1993bhmw.conf....1W

Page: using his earlier results about entropy of a subsystem, he argues that if black hole evaporation can be described by an S matrix,
information may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in the Planck mass:
"Information in black hole radiation"
http://adsabs.harvard.edu/abs/1993PhRvL..71.3743P

Anglin, Laflamme, Paz, Zurek: A harmonic oscillator in a superposition of states, coupled to a linear quantum field. When the oscillator settles to
its ground state, the quantum field is in a pure state, but that can only be seen by measuring nonlocal operators which are computed explicitly here:
"Decoherence and recoherence in an analogue of the black hole information paradox"
http://adsabs.harvard.edu/abs/1995PhRvD..52.2221A

Why I changed my mind about whether black holes swallow information: AdS/CFT as an example shook my faith, and Marolf generalized the AdS/CFT
scenario to argue that in any generally covariant theory of gravity, the total Hamiltonian lives in the boundary algebra of observables, so that algebra
must evolve unitarily, which seems to rule out information loss as viewed from the boundary:
"Unitarity and holography in gravitational physics"
http://adsabs.harvard.edu/abs/2009PhRvD..79d4010M


From Aron Wall: References for Quantum Horizon Fluctuations working group:
  • Here is my proof of the GSL for semiclassical horizons based on the method of restricting fields to the horizon. The paper is on the arxiv, but this version has some corrected numerical factors. Section 2 outlines the proof, while Sections 3-5 describe the details of field theory on a null surface.
  • A review article by Matthias Burkardt explaining light front quantization.
  • My attempt to calculate the size of fluctuations in the intrinsic null geometry of the horizon using null surface techinques, in a coordinate system where the horizon location remains fixed.

Other approaches mentioned during discussion:
  • Don Marolf's estimate of horizon fluctuations as a UV entanglement cutoff, based on location of the horizon relative to the area-radius coordinate.
  • Many articles by L.H. Ford on this subject.
  • R. Brustein & M. Hadad paper mentioned during discussion.

Please feel free to add additional references!


References for working group "Quantum framework for eternal inflation and dS/CFT"

Here are some references containing more details of the material I summarized in the discussion IR issues in dS: local vs. global. - Steve Giddings

Semiclassical relations and IR effects in de Sitter and slow-roll space-times (w/ M. Sloth) Describes connection between semiclassical picture of growing perturbations/variance (scalar, tensor) in inflation and IR growth in loops; this growth is similar to that which drives self-reproducing inflation. Leading IR contributions to loops can be derived from calculations using a semiclassical picture (with explicit checks). Points out apparent breakdown of perturbation theory at times ~RS.

Cosmological diagrammatic rules (w/ M. Sloth) introduces diagrammatic rules for in-in perturbation theory, that simplify calculations.

Cosmological observables, IR growth of fluctuations, and scale-dependent anisotropies (w/ M. Sloth) More details of the local vs. global perspective. In particular spells out more details of how potentially large long-wavelength fluctuations can be removed for the purposes of describing "IR-safe" local observables. Investigates "scale-dependent" metric and its role in such definitions, and corresponding renormalization group equations. Describes possible observational window to IR growth of fluctuations, through local statistical anisotropy one could look for with 21 cm observations.

Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes (w/ M. Sloth) discusses the problem of defining quantum observables sensitive to global features of the geometry, such as large accumulated IR fluctuations. Investigates proposed gauge-invariant two-point functions based on geodesic length between points (and related constructions), and long-time/distance breakdown of such constructions due to accumulated fluctuations.



Monday April 16 at 1:30pm in the Auditorium we had a Discussion group on the topic:

What part of the asymptotically AdS gravitational phase space is dual to a CFT?


The discussion was motivated by a puzzle: there are apparently an arbitrarily large "number" of classical configurations of bulk gravity at arbitrarily low energy,
at least in asymptotically flat spacetime, which exist thanks to red shifting in a gravitational well. The CFT dual to AdS gravity seems to lack such states. The
discussion was aimed at understanding the nature and meaning of this discrepancy.
====================================
Ted Jacobson

Attempt to list the main possibilities:

1. Duality encompasses the entire phase space

In this case something must explain why the apparently over-entropic states are not present. This explanation might be:

- the states are not actually present in classical phase space after enforcing constraints and quotienting by diffeos
- the states occupy small phase space volume so don't survive quantization
- semiclassical state counting by phase space volume fails to be accurate
- the CFT has "hidden sectors" at low energy and includes these states

2. Duality encompasses only part of the phase space

In this case something must explain what part is included, and why, and what determines which part is included?
Possible answers:

- states with a global event horizon not included (this condition is nonlocal in time)
- states with singular past and future not included
- some combination of the above

I would add a couple of questions: if possibility 2. holds,

- can this be understood via Maldacena's original argument in favor of the duality?
- consider a one-parameter family of gravitational states that begins in the AdS vacuum, and gradually builds up monsters with more and more entropy.
what happens to the dual state in the CFT as the monstrous region of phase space is approached?
===============================
Steve Hsu

Monster papers:
http://arxiv.org/abs/0706.3239
http://arxiv.org/abs/0803.4212
http://arxiv.org/abs/0908.1265

Also: R. D. Sorkin, R. M. Wald and Z. J. Zhang, Gen. Rel. Grav. 13, 1127 (1981)

Slides I displayed:
http://duende.uoregon.edu/~hsu/talks/bitbrane_monster_talk.pdf

Summary: In classical GR one can construct apparently compact objects with fixed ADM mass but arbitrarily large entropy.
These objects collapse into black holes but have more entropy than the area of the resulting black hole.
================================
Steve Giddings

In the discussion, I argued that charged black holes sharply illustrate problems closely linked to those of "monsters."
Specifically, if one follows semiclassical reasoning, they also have an unbounded number of internal states.
This apparently leads to an infinity in their contribution to a thermal ensemble, and to infinite pair production.

Some of these arguments were spelled out in a paper "Why aren't black holes infinitely produced?," http://arXiv.org/abs/hep-th/9412159 .
This paper discusses different ways of treating pair production, including via an instantonic description, which has a parallel for magnetic monopoles.
(See references therein.) It also outlines an effective field theory description of such charged black holes, or more general black hole remnants.
(See also earlier refs. such as http://arxiv.org/abs/hep-th/9304027). It would be interesting if some significant loophole could be found in these arguments.

A related set of considerations, involving infinite renormalization of Newton's constant due to remnants propagating in loops, is Susskind's paper
"Trouble For Remnants," http://arXiv.org/abs/hep-th/9501106 .

As noted, a mismatch between the "classical phase space" and the boundary gauge theory of AdS/CFT could arise either because such configurations
do not appear among the true quantum states of the bulk theory, or because of the lack of a precise correspondence between the bulk Hilbert space
and the boundary Hilbert space -- or both. (Some aspects of the latter question are discussed in http://arXiv.org/abs/arXiv:1105.6359 .)
==================================
Alex Maloney

Unfortunately I don't have any good references for the second part of my comments. For the first part, I suppose that a good reference is
http://arxiv.org/abs/1107.5098
===================================