# Physics 776---Advanced Gravitation Theory---Spring 2005

Black Hole Thermodynamics

Project Ideas

Look into the black hole uniqueness theorems and the arguments that a stationary
black hole horizon should be a Killing horizon.

Look into the extension of the area theorem to nonsmooth horizons (highly mathematical).

Gedanken experiments to destroy a black hole:
see Hubeny, Overcharging a Black Hole and Cosmic Censorship
(http://arxiv.org/abs/gr-qc/9808043) and references therein.
Hubeny (who was a Maryland undergrad before going to Santa Barbara for grad school)
noticed that if one neglects the gravitational back reaction, it appears possible to overcharge
a black hole so that Q>M, by injecting mass and charge into the black hole. She began but did not
finish the study of the back reaction. You could learn about the background of this issue, the
old papers, and Hubeny's paper and the follow-ups, if any. Then, I have an idea for an extension:
repeat her idea but for spin instead of charge. That it, try to overspin a black hole by throwing
in a point particle with orbital angular momentum, or one with instrinsic spin (using the
Papapetrou equation). This extension to spinning black holes would be publishable, provided
it has not yet been done. A quick look did not reveal to me that anyone has done it.

Domain of validity of the first law of black hole mechanics:
The physical process version of the first law was derived for situations where the change is a
"small" perturbation. The exact meaning of "small" in this context wasn't spelled out very clearly.
There is more on this in my article Horizon Entropy. You could look into this question, learn what
has been said, and try to find a nice controlled example where you can go from small to not small
perturbation and see exactly how the first law breaks down. To begin with you can look at the
situation in hw4, in which a spherical shell of mass M collapses, followed by another shell of
mass Delta M, and see how the relevant notions of "smallness" relate to the time of arrival of
Delta M, and the ratio (Delta M)/M.  This is a somewhat open-ended project.

T. Damour's equation for the dissipative evolution of a horizon:
understand the derivation, and the conditions under which the behavior holds.
Need to find the right reference. But a start (and possibly and end) could
be the book, Black Holes: The Membrane Paradigm.

The Irreversible Thermodynamics of Black Holes,
P. Candelas & D.W. Sciama
http://prola.aps.org/abstract/PRL/v38/i23/p1372_1?qid=b7bbb03ca0332f0a&qseq=5&show=10

Report on this paper, explain fully the connection to the fluctuation-dissipation relation.
(I'm not  sure how logically coherent this paper really is.) The paper includes quantum
field theory aspects.

Study and report on Wald's Noether charge method to determine the black hole entropy in any generally
covariant gravitational theory. See references, eg, in one of Wald's review articles.

In response to Hawking's original suggestion that black hole evaporation sends pure quantum
states to mixed states, Banks, Peskin, and Susskind  argued that generically such evolution
will produce causality violations ot violent violations of energy-momentum conservation.
In a response, Unruh and Wald argued that such violations can be kept unobservably small,
or even eliminated if one does not assume the evolution is a Markov process, i.e. if one allows
for it to have a memory. Read these classic papers and report on the story in some detail,
highlighting what you think are the most important points.

The references:
S.W. Hawking, BREAKDOWN OF PREDICTABILITY IN GRAVITATIONAL COLLAPSE, Phys.Rev.D14:2460-2473,1976
S.W. Hawking, THE UNPREDICTABILITY OF QUANTUM GRAVITY, Commun.Math.Phys.87:395,1982
Tom Banks, Leonard Susskind, Michael E. Peskin, DIFFICULTIES FOR THE EVOLUTION OF PURE STATES INTO MIXED STATES, Nucl.Phys.B244:125,1984
William G. Unruh, Robert M. Wald, ON EVOLUTION LAWS TAKING PURE STATES TO MIXED STATES IN QUANTUM FIELD THEORY, Phys.Rev.D52:2176-2182,1995 e-Print Archive: hep-th/9503024.

Trans-Planckian issue: Review some of the work on the effect of modified dispersion relations on Hawking radiation or on the primordial fluctuation spectrum in cosmology. For a start on the references, see my Valdivia lecture notes, http://arxiv.org/abs/gr-qc/0308048. Then you can look in SPIRES at the papers referencing those papers.

Report on the analysis of the Hawking-Page phase transition in which hot AdS becomes Schwarzschild AdS. References:
S.W. Hawking, Don N. Page, THERMODYNAMICS OF BLACK HOLES IN ANTI-DE SITTER SPACE, Commun.Math.Phys.87:577,1983.
E. Witten, Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories http://arxiv.org/abs/hep-th/9803131

Aside from the famous Hawking-Page phase transition , there can be a less familiar phase transition where a "small" black hole forms. This can be stable since AdS acts like a box (see hw5 for the flat spacetime analog). Report on the reasoning and do some of the calculations justifying this, based on the paper by Gary Horowitz, http://arxiv.org/abs/hep-th/9910082, Comments on Black Holes in String Theory.  I believe the nature of this other phase is not yet understood in the context of the AdS/CFT correspondence. Try to find out what the status is.

String-black hole correspondence for Schwarzschild black holes. See

SELFGRAVITATING FUNDAMENTAL STRINGS.
By Gary T. Horowitz (UC, Santa Barbara ), Joseph Polchinski (Santa Barbara, KITP ),. NSF-ITP-97-097, Jul 1997. 20pp.
Published in Phys.Rev.D57:2557-2563,1998
e-Print Archive: hep-th/9707170

A CORRESPONDENCE PRINCIPLE FOR BLACK HOLES AND STRINGS.
By Gary T. Horowitz (UC, Santa Barbara ), Joseph Polchinski (Santa Barbara, KITP ),. NSF-ITP-96-144, Dec 1996. 25pp.
Published in Phys.Rev.D55:6189-6197,1997
e-Print Archive: hep-th/9612146

QUANTUM STATES OF BLACK HOLES.
By Gary T. Horowitz (UC, Santa Barbara ),. UCSBTH-97-06, Dec 1996. 33pp.
Presented at Symposium on Black Holes and Relativistic Stars (dedicated to memory of S. Chandrasekhar), Chicago, IL, 14-15 Dec 1996.
In *Wald, R.M. (ed.): Black holes and relativistic stars* 241-266.
e-Print Archive: gr-qc/9704072

SELFGRAVITATING FUNDAMENTAL STRINGS AND BLACK HOLES.
By Thibault Damour (IHES, Bures-sur-Yvette ), Gabriele Veneziano (CERN ),. IHES-P-99-54, Jul 1999. 28pp.
Published in Nucl.Phys.B568:93-119,2000
e-Print Archive: hep-th/9907030

Isolated and Dynamical Horizons formalism: see and references therein:

ISOLATED AND DYNAMICAL HORIZONS AND THEIR APPLICATIONS.
By Abhay Ashtekar (Penn State U. &Santa Barbara, KITP &Potsdam, Max Planck Inst. &Schrodinger Inst., Vienna ), Badri Krishnan (Potsdam, Max Planck Inst. &Schrodinger Inst., Vienna ),. Jul 2004. 77pp.
Published in Living Rev.Rel.7:10,2004
e-Print Archive: gr-qc/0407042

V.P. Frolov, M.A. Markov and V.F. Mukhanov, Through a black hole into a new
universe?, Phys. Lett. B 216 (1989) 272.

HOW MANY NEW WORLDS ARE INSIDE A BLACK HOLE?
By Claude Barrabes (Tours U. &Meudon Observ. ), Valeri P. Frolov (Alberta U. &Lebedev Inst. ),. ALBERTA-THY-30-95, Nov 1995. 24pp.
Published in Phys.Rev.D53:3215-3223,1996
e-Print Archive: hep-th/9511136

UNIVERSE GENERATION FROM BLACK HOLE INTERIORS.
By Damien A. Easson ,Robert H. Brandenberger (Brown U. ),. BROWN-HET-1245, Mar 2001. 6pp.
Published in JHEP 0106:024,2001
e-Print Archive: hep-th/0103019

Smooth transitions from Schwarzschild to de Sitter
Authors: Steven Conboy ,Kayll Lake
http://arxiv.org/abs/gr-qc/0504036