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Black Holes: New Perspectives from Higher Dimensions

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Black Holes: New Perspectives from Higher Dimensions Black Holes: New Perspectives from Higher Dimensions Nidal Haddad ADVERTIMENT. La consulta d’aquesta tesi queda condicionada a l’acceptació de les següents condicions d'ús: La difusió d’aquesta tesi per mitjà del servei TDX (www.tdx.cat) ha estat autoritzada pels titulars dels drets de propietat intel·lectual únicament per a usos privats emmarcats en activitats d’investigació i docència. No s’autoritza la seva reproducció amb finalitats de lucre ni la seva difusió i posada a disposició des d’un lloc aliè al servei TDX. No s’autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant al resum de presentació de la tesi com als seus continguts. En la utilització o cita de parts de la tesi és obligat indicar el nom de la persona autora. ADVERTENCIA. 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On having consulted this thesis you’re accepting the following use conditions: Spreading this thesis by the TDX (www.tdx.cat) service has been authorized by the titular of the intellectual property rights only for private uses placed in investigation and teaching activities. Reproduction with lucrative aims is not authorized neither its spreading and availability from a site foreign to the TDX service. Introducing its content in a window or frame foreign to the TDX service is not authorized (framing). This rights affect to the presentation summary of the thesis as well as to its contents. In the using or citation of parts of the thesis it’s obliged to indicate the name of the author. Black Holes: New Perspectives from Higher Dimensions Mem`oriapresentada per a optar al t´ıtolde Doctor en F´ısicaper Nidal Haddad Departament de F´ısica Fonamental i Institut de Ci`enciesdel Cosmos, Universitat de Barcelona, Mart´ıi Franqu`es1, E-08028 Barcelona Programa de doctorat de F´ısica Universitat de Barcelona Dirigida pel Prof. Roberto Emparan To my parents i ii Contents 1 Resum en catal`a 1 2 Introduction 5 2.1 General relativity in 4 dimensions . 5 2.2 String theory predicts extra dimensions . 6 2.3 Black holes in higher dimensions . 7 2.4 AdS/CFT correspondence . 9 2.5 Fluid/Gravity correspondence . 11 2.6 Holography in flat space . 13 2.7 Outline of thesis . 14 3 Blackfolds 17 3.1 General idea . 17 3.2 Boosted black p−branes . 18 3.3 Effective stress tensor . 19 3.4 Equations of motion for blackfolds . 20 4 Topology change in general relativity 21 4.1 Prelude . 21 4.2 Phases of Kaluza-Klein black holes . 22 4.3 Black string−black hole transition . 23 4.4 Other topological transitions . 25 5 Black Brane Viscosity and the Gregory-Laflamme Instability 27 5.1 Introduction and Summary . 27 5.2 Hydrodynamic perturbations of black branes . 31 5.2.1 Preliminaries . 31 5.2.2 Solving the perturbation equations . 34 5.2.3 Viscous stress tensor . 37 5.3 Damped unstable sound waves and the Gregory-Laflamme instability . 38 iii 5.4 Discussion . 41 6 Self-similar critical geometries at horizon intersections and mergers 43 6.1 Introduction . 43 6.2 Intersection of black hole and deSitter horizons . 46 6.2.1 Horizon intersection . 46 6.2.2 Isothermal solutions . 49 6.3 Merged solution . 51 6.4 Critical geometries for other topology-changing transitions . 55 6.5 Concluding remarks . 58 7 Summary of results 61 A Equal-temperature limit 63 B General black hole-deSitter intersections 65 iv Acknowledgements I would like to thank Roberto Emparan for supervising me throughout the four years of the PhD period, for teaching me, and for letting me work on interesting and diverse problems. I would like to thank also the members of our group, the "Gravitation and Cosmology Group" of the university of Barcelona, Enric Verdaguer, Jaume Garriga, David Mateos, and Bartomeu Fiol. It was a pleasure and of great help during my PhD period to have been friends, and office mates at the same time, with Guillem Perez, Nico geisel, Martin Goethe, Maria Aznar, and Markus Frob. It was a pleasure as well to have Sudipto Muhuri and Paolo Indescai as friends. I would like to thank Joan Camps for both friendship and collaboration. Special thanks are for my friend Hicham Bakkali for excellent times and encouragement. Finally, I would like to thank my parents, Fateen and Ahlam, for their very generous support, for their full trust in me, and for their permanent encouragment during my PhD period, without whom I would not have been able to reach this stage. The same is true for my family as a whole, my parents, my beloved little sister, Fatima Al-Zahraa, my brother (and friend) Alaa and his wife Donia. v vi Chapter 1 Resum en catal`a Malgrat el seu `exita nivell cl`assic,la relativitat general s'enfronta a problemes de no- renormalitzabilitat a nivell qu`antic. No obstant, prediu l'exist`encia de forats negres, que s´onobjectes t`ermics que s'espera que continuin existint en una teoria satisfact`oria de gravetat qu`antica. La seva consist`enciamatem`aticarequereix que l'espai-temps tingui deu dimensions, i d'aquesta manera motiva l'estudi de la relativitat general, i en particular els forats negres, en dimensions altes. Aquest ´esel tema central de la nostra tesi. A m´es,l'adveniment de la correspond`enciaAdS/CFT, que relaciona una teoria de gravetat amb una teoria qu`antica de camps en una dimensi´omenys, ha incrementat encara m´esl'inter`esen la gravetat en dimensions altes. Comparada amb la relativitat general en quatre dimensions, que ha estat `ampliament estudiada i investigada els darrers anys, la relativitat general en dimensions m´esaltes t´emoltes caracter´ıstiques noves i interessants. La unicitat ´esuna propietat de la relativitat general en quatre dimensions que no continua sent v`alidaen dimensions m´esaltes. Una altra propietat relacionada amb aquesta ´esque en quatre dimensions els forats negres nom´espoden tenir horitzons amb topologia esf`erica,mentre que en dimensions m´esaltes els objectes negres poden tenir tamb´ealtres topologies. Els anells negres s´onuna manifestaci´od’aix`o.Les dues noves propietats esmentades donen lloc a transicions de fase topol`ogiquesa l'espai de fases dels forats negres en dimensions altes, que ´esun dels temes que considerem i als quals contribuim en aquesta tesi. L'exist`enciad'objectes negres estesos en dimensions altes, anomenats p-branes ne- gres, ´esun tema important i fonamental. Se sap que aquests objectes s´ondin`amicament inestables. Per tant, la q¨uesti´ode cap on condueix aquesta inestabilitat ha esdevingut un problema important. Quin ´esl'estat final? Aquesta inestabilitat es coneix com la inestabilitat de Gregory-Laflamme i ´esun altre tema que investiguem a la nostra tesi, i que relacionem amb un tipus de correspond`enciaentre fluids i gravetat a l'espai-temps 1 pla. L'exist`enciade p-branes negres s'atribueix al fet que en relativitat general en di- mensions altes hi ha forats negres que poden rotar de manera arbitr`ariament r`apida. Es´ a dir, no hi ha un an`alegde la cota de Kerr en quatre dimensions, que impedeix que els forats negres donin voltes molt de pressa. La rotaci´or`apida,per altra banda, que ´espossible en dimensions m´esaltes t´el'efecte d'aplanar l’horitz´odel forat negre al llarg del pla de rotaci´o,i per tant en el limit de velocitats altes s'apropa a la geometria de la p-brana negra. Al cap´ıtol 3 donem una breu introducci´oa l'estudi de forats negres en dimensions m´esaltes per mitj`ade les anomenades \blackfolds". Discutim les raons per les quals hom pot fer servir nous m`etodes aproximats en dimensions m´esaltes. Introduim els objectes b`asicsde l'enfoc amb blackfolds, les p-branes negres impulsades, i expliquem com l'enfoc amb blackfolds es pot fer servir per construir a partir d'elles noves solucions estacion`ariesde les equacions del camp gravitatori amb noves topologies, i com es pot fer servir tamb´eper construir solucions din`amiques. Al cap´ıtol4 donem una breu introducci´oal tema dels canvis de topologia en rel- ativitat general. Discutim les fases del forat negre de Kaluza-Klein, la fase de corda negra homog`enia,la fase de corda negra inhomog`eniai fase de forat negre localitzat. Expliquem el mecanisme pel qual apareix una transici´ode fase topol`ogicaquan hom es mou per l'espai de fases des d'una corda negra fins a un forat negre localitzat. Al cap´ıtol5 hem aconseguit formular un tipus de correspond`enciaentre fluids i gravetat a l'espai pla. Hem trobat un mapa entre una p-brana negra impulsada fluc- tuant i un fluid visc´osrelativista situat a l’infinit espacial. Es´ a dir, hem construit una soluci´ode les equacions d'Einstein al buit d'una p-brana negra din`amicafins a primer ordre en derivades.
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