Evolution of Black Holes in Anti-de Sitter Spacetime and the Firewall Controversy PDF
Preview Evolution of Black Holes in Anti-de Sitter Spacetime and the Firewall Controversy
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 Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria (cid:129) They must be written in good English. (cid:129) ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineeringandrelatedinterdisciplinary fields such asMaterials,Nanoscience, Chemical Engineering, Complex Systems and Biophysics. (cid:129) The work reported in the thesis must represent a significant scientific advance. (cid:129) Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. (cid:129) They must have been examined and passed during the 12 months prior to nomination. (cid:129) Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. 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More information about this series at http://www.springer.com/series/8790 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 ©Springer-VerlagBerlinHeidelberg2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper Springer-VerlagGmbHBerlinHeidelbergispartofSpringerScience+BusinessMedia (www.springer.com) 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
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