Gravitation Theory---Spring 2005
Black Hole Thermodynamics
Look into the black hole
uniqueness theorems and the arguments that a
black hole horizon should be a Killing horizon.
Look into the extension of the
area theorem to nonsmooth horizons
Gedanken experiments to destroy a
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
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
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
T. Damour's equation for the
dissipative evolution of a horizon:
understand the derivation, and the conditions under which the behavior
Need to find the right reference. But a start (and possibly and end)
be the book, Black Holes:
The Membrane Paradigm.
The Irreversible Thermodynamics
of Black Holes,
P. Candelas & D.W. Sciama
Report on this paper, explain fully the connection to the
(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
covariant gravitational theory. See references, eg, in one of Wald's
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
In a response, Unruh and Wald argued that such violations can be kept
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.
S.W. Hawking, BREAKDOWN OF PREDICTABILITY IN GRAVITATIONAL COLLAPSE,
S.W. Hawking, THE UNPREDICTABILITY OF QUANTUM GRAVITY,
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
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
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.
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.
Published in Living Rev.Rel.7:10,2004
e-Print Archive: gr-qc/0407042
Baby Universe generation inside
black holes: start with:
V.P. Frolov, M.A. Markov and V.F. Mukhanov, Through a black hole into a
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