Evolution of Black Holes in Anti-de Sitter Spacetime and the Firewall Controversy

236 Pages·2016·4.75 MB·English

by  Yen Chin Ong (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Yen Chin Ong

Evolution of Black
Holes in Anti-de
Sitter Spacetime
and the Firewall
Controversy
Springer Theses
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Yen Chin Ong
Evolution of Black
Holes in Anti-de Sitter
Spacetime and the Firewall
Controversy
Doctoral Thesis accepted by
National Taiwan University, Taipei, Taiwan
123
Author Supervisor
Dr. Yen ChinOng Prof. PisinChen
Nordic Institute for TheoreticalPhysics Department ofPhysics, Leung Centerfor
Stockholm Cosmology andParticle Astrophysics
Sweden Graduate Institute of Astrophysics,
National Taiwan University
Taipei
Taiwan
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-662-48269-8 ISBN978-3-662-48270-4 (eBook)
DOI 10.1007/978-3-662-48270-4
LibraryofCongressControlNumber:2015947794
SpringerHeidelbergNewYorkDordrechtLondon
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As regards this little key, it is the key to the
small room at the end of the long passage on
the lower floor. You may open everything,
you may go everywhere, but I forbid you to
enter this little room. And I forbid you so
seriously that if you were indeed to open the
door, I should be so angry that I might do
anything.
La Barbe Bleue, Charles Perrault
This dissertation is dedicated
to the 41st anniversary of Hawking
Radiation, and the 100th anniversary
of General Relativity.
’
Supervisor s Foreword I
The information loss paradox in black hole physics has been an outstanding
problem for 40 years, ever since Hawking’s landmark paper titled “Breakdown of
Predictability inGravitational Collapse”in1976.Therehavebeenmany proposals
overtheyears,rangingfrom“itisfineforinformationtobelost”to“informationis
recovered at late time via subtle entanglements in the Hawking radiation.” The
debate became evenmore heated in2012,when Almheiri, Marolf,Polchinski, and
Sully argued that (under some seemingly reasonable assumptions) if Hawking
radiation contains information, the horizon of a black hole will eventually be
shrouded by a high energy curtain—the “firewall”, which would burn up any
in-falling observer.
In order to track the information content, it is important to understand the
evolution of black holes as they undergo Hawking evaporation. However, the end
stateofblackholeevaporationisnotoriouslydifficulttostudyinasymptoticallyflat
spacetimes. The usual Schwarzschild black hole has a Hawking temperature that
scales inversely proportional to its mass: T /1=M. Therefore as the black hole
becomes smaller its temperature increases. In addition, curvature also becomes
unbounded as the black hole size shrinks towards zero. If one thinks of general
relativity as an effective field theory, this means that new physics may come in at
some point, and the attempt to understand the end state of the evaporation will
require some knowledge of the new physics, if not the entire mastery of quantum
gravity.
Thefirewalldebateisthereforethesharpestwhenformulatedinthecontextofa
certaintopological black holes inanti-de Sitter space, namely black holes withflat
eventhorizons;forthecurvatureatthehorizonsoftheseblackholesremainssmall
throughouttheirentireevolutionunderHawkingevaporation.Morespecifically,the
mainworkinthisthesisconcernselectricallychargedblackholeswithflathorizons
in anti-de Sitter space, since charged black holes typically have a much longer
lifetime than their neutral counterparts. This is important because Harlow and
Haydenhaveproposedthatfirewallscanonlybeformedifthereisenoughtimefor
an external observer to decode the information from the Hawking radiation. With
ix
x Supervisor’sForewordI
their longer lifetimes, charged black holes are therefore a threat to the
Harlow-Hayden proposal to avoid firewalls from ever forming. With careful
mathematicalmodeling,thisthesisdemonstratesthatsuchadangerisneveractually
realized. On the contrary, these black holes always evolve towards the extremal
limit, and are then destroyed by quantum gravitational effects (a stringy version
of the Schwinger effect that involves brane-pair production). These happen at a
timescalemuchshorterthanthetimerequiredtodecode Hawkingradiationsothat
firewalls never set in.
Thelastpartofthethesisdealswithacertaingravitationalconfigurationcalleda
“monster,” which was first proposed by Stephen Hsu and David Reeb in 2007.
A monster is a nonblack hole configuration that has an even higher (in fact, arbi-
trarily large) entropy than the Bekenstein-Hawking entropy of a black hole of the
same mass. The nature of the Bekenstein-Hawking entropy, which is proportional
to the black hole area, is also an open problem; there are two interpretations: the
strong form and the weak form. The strong form interpretation is the most
well-known one—the Bekenstein-Hawking entropy is the maximum entropy a
black hole can have; and the interior degrees of freedom are somehow already
encoded in the area. The weak form, on the other hand, states that the
Bekenstein-Hawking entropy is not sensitive to the interior at all.
In fact, in some proposals that involve black hole remnants or baby universes,
informationisnevertrulylostbutisstoredinsideblackholes.Monstersprovidethe
arena to study super-entropic objects, which could provide better insight into the
natureofblackholeentropyanditsinformationcontent.Inthisthesis,monstersin
anti-de Sitter space were considered. Such configurations are problematic for the
AdS/CFTcorrespondencesincetherewillnotbeenoughdegreesoffreedomonthe
boundary to encode the bulk degrees offreedom, due to the fact that monsters can
have arbitrarily large entropy. Fortunately, it was found that brane-pair production
in string theory implies that, at least in the best understood case, such monster
configurations are unlikely to exist.
Taipei, Taiwan Pisin Chen
June 2015
Foreword II
The past decade has seen a remarkable and unexpected development in the theory
ofstrongly-coupledsystems,particularlyinthephysicsoftheQuark-GluonPlasma
(QGP). The traditional lattice methods continue to be important, in fact ever more
so with increasing computational power; but, for well-known technical reasons,
theyhavenotyetgivenacompletelysatisfactoryaccountofallregionsofthequark
matter phase diagram. In particular, they encounter serious difficulties when the
baryonicchemicalpotentialμ islarge,asitisinsomecurrentandmanyprojected
B
experimental programs involving collisions of heavy ions.
It was therefore of the greatest interest when Witten proposed in 1998 that the
then new methods of gauge-gravity duality might be applied to such systems. In
thistheory,theplasmaismodeledbyacertainconformalfieldtheorydefinedonthe
conformalboundaryofcertainasymptoticallyanti-deSitterspacetimes(the“bulk”).
The bulk physics is described by string theory, but, under certain well-defined
circumstances(thestringcouplingandtheratioofthestringlengthscaletotheAdS
curvature scale L are small) it may be possible to neglect stringy objects, such as
“branes,” in the bulk. In such cases, the bulk can be understood by studying
relatively simple, weakly coupled systems in the bulk, such as electromagnetic
fields around semi-classicalblack holes. The dualitythen transformsan intractable
problem in the boundary field theory to a problem in semi-classical general rela-
tivity, where a vast array of sophisticated techniques are available.
Dr. Ong’s thesis reminds us, however, that while it may be consistent to ignore
stringy objects in the bulk, it may not be. In particular, he reminds us that it is not
correcttoassumethisforasymptoticallyAdSblackholeswhicharehighlycharged
(yet still sub-extremal). Such a black hole is a perfectly respectable object in
classical general relativity, but not in string theory: even if one declares that the
bulkisfreeofbranesinitially,onefindsthat,forasufficientlyhighlychargedblack
hole, branes will be produced in the bulk spontaneously, by a sort of generalized
version of Schwinger pair-production. These branes will themselves modify the
blackholegeometry,andsotheassumedexistenceofalong-livedblackholeofthis
sortisruledout.Thisisanunusualexampleofgauge-gravitydualitybeingapplied
xi