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Graduate Texts in Physics Daniel Grumiller Mohammad Mehdi Sheikh-Jabbari Black Hole Physics From Collapse to Evaporation Graduate Texts in Physics SeriesEditors KurtH.Becker,NYUPolytechnicSchoolofEngineering,Brooklyn,NY,USA Jean-MarcDiMeglio,MatièreetSystèmesComplexes,BâtimentCondorcet,Université ParisDiderot,Paris,France SadriHassani,DepartmentofPhysics,IllinoisStateUniversity,Normal,IL,USA MortenHjorth-Jensen,DepartmentofPhysics,Blindern,UniversityofOslo,Oslo, Norway BillMunro,NTTBasicResearchLaboratories,Atsugi,Japan RichardNeeds,CavendishLaboratory,UniversityofCambridge,Cambridge,UK WilliamT.Rhodes,DepartmentofComputerandElectricalEngineeringandComputer Science,FloridaAtlanticUniversity,BocaRaton,FL,USA SusanScott,AustralianNationalUniversity,Acton,Australia H.EugeneStanley,CenterforPolymerStudies,PhysicsDepartment,Boston University,Boston,MA,USA MartinStutzmann,WalterSchottkyInstitute,TechnicalUniversityofMunich, Garching,Germany AndreasWipf,InstituteofTheoreticalPhysics,Friedrich-Schiller-UniversityJena, Jena,Germany GraduateTextsinPhysicspublishescorelearning/teachingmaterialforgraduate-and advanced-levelundergraduatecoursesontopicsofcurrentandemergingfieldswithin physics, both pure and applied. These textbooks serve students at the MS- or PhD-levelandtheirinstructorsascomprehensivesourcesofprinciples,definitions, derivations,experimentsandapplications(asrelevant)fortheirmasteryandteaching, respectively.Internationalinscopeandrelevance,thetextbookscorrespondtocourse syllabisufficientlytoserveasrequiredreading.Theirdidacticstyle,comprehensive- nessandcoverageoffundamentalmaterialalsomakethemsuitableasintroductions orreferencesforscientistsentering,orrequiringtimelyknowledgeof,aresearchfield. Daniel Grumiller · Mohammad Mehdi Sheikh-Jabbari Black Hole Physics From Collapse to Evaporation DanielGrumiller MohammadMehdiSheikh-Jabbari InstituteforTheoreticalPhysics SchoolofPhysics TUWien InstituteforResearchinFundamental Vienna,Austria Sciences Tehran,Iran ISSN1868-4513 ISSN1868-4521 (electronic) GraduateTextsinPhysics ISBN978-3-031-10342-1 ISBN978-3-031-10343-8 (eBook) https://doi.org/10.1007/978-3-031-10343-8 ©SpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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EHTCollaborationunderCCBY-ND4.0license ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland MohammadMehdiSheikh-Jabbaridedicates thisbooktohiswifeYasamanFarzanforall hersupportandencouragement DanielGrumillerdedicatesthisbooktohis parentsIngoGrumiller,WilfriedRaunikar, andHelgaWeuleforpassingontheir curiosityaboutLife,theUniverse,and Everything Foreword The study of black holes arguably began in 1783 with John Michell. At the time, Michell was the rector of St. Michael’s church in the Yorkshire village of Thorn- hill. Prior to this, he had been educated and become a fellow of Queens’ College CambridgeandalsohadbeenWoodwardprofessorofgeologyinCambridge.How- ever, fellows of Cambridge colleges at the time were required to be celibate and so he migrated on marriage, as many at the time did, to the church. His clerical duties were sufficiently light that he was able to continue his scientific studies. In the Proceedings of the Royal Society, he laid out the possibility that there were starsthatcouldnotbeseen.HisreasoningwasentirelyNewtonian.Hewasableto calculate the escape velocity of a particle from the surface of a massive body. He knew that light had large, but finite, velocity as had been shown in the previous century by Rømer. His conclusion was that if a star was sufficiently condensed, then it would be invisible. Supposing that the star had mass M, then if its radius R was such that 2G M R < N c2 where G is Newton’s gravitational constant and c is the speed of light, then it N wouldbeinvisible.Remarkably,thesameformulaholdsingeneralrelativity.Some 14yearslaterin1796,PierreLaplace,workingindependently,publishedasimilar result from the other side of the English Channel. It was not until Einstein proposed the general theory of relativity that mat- ters progressed. As soon as his theory became known, Karl Schwarzschild found in 1915 the exact solution of Einstein’s field equations that bears his name. His solution is a spacetime metric that contains a black hole. For a long time, there were discussions about whether the horizon was singular or not, and whether the spacetime singularity at the center of the black hole was unphysical. Despite the uncertainty about whether the Schwarzschild metric was physically acceptable, in 1939 J. Robert Oppenheimer and Hartman Snyder showed that, under certain cir- cumstances,astarcouldcollapsetoformablackhole.Nevertheless,considerable skepticism about the possible existence of black holes remained until the early 1970s. vii viii Foreword A revolution in our understanding of general relativity and black holes, in particular, started in the late 1950s driven by John Archibald Wheeler in Princeton. Heseemstohavebeenmotivatedbyattemptstounderstandthefinalstateofstars and also began to formulate a quantum theory of gravity. This started a period of great excitement. Two key events were that Roger Penrose proved the first singularity theorem in 1965. He showed that if a trapped surface formed, then a spacetime singularity must exist. This result removed one of the possible stum- bling blocks in understanding black holes. In Oppenheimer–Snyder collapse, one doesformaspacetimesingularity,butsuchathingmighthavebeenaconsequence of assuming exact spherical symmetry, something which cannot happen in nature. Penrose’sresultshowedthatsingularitieswouldformwithoutmakinganyassump- tions about spatial symmetry. Also in 1965, Roy Kerr found the spacetime metric that describes the most general stationary black hole in an asymptotically flat spacetime.Theseresultstriggeredaflurryofkeyresultsinclassicalgeneralrelativ- ity.Theyledtoanunderstandingoftheastrophysicsofblackholes.Thediscovery of black hole X-ray sources as stellar remnants, quasars, the black holes in the centers of galaxies as conclusively proved by the recent results of the event hori- zontelescope,andtheproductionanddetectionofgravitationalwavesincollisions involving black holes have removed any uncertainty about their existence. However,therearestillchallenges.Hawkingshowedthatblackholesemitradi- ation that appears to be thermal. This was perhaps the first successful result in quantumgravityandithasgeneratedanenormousfollow-upliterature.Thedeep- est puzzle is the information paradox. Quantum mechanical information appears to be destroyed as a black hole evaporates away. Most of us believe that this cannot happen, largely because of the incredible successes that quantum mechanics has. Nevertheless, the subject is still open, and there are many that believe that informationisdestroyed.Therehasbeenalotofrecentprogressandinparticular, the beginning of our understanding of holography, the discovery of soft hair, and the application of rigorous quantum information theory is helping an exploration of this problem. This book provides an excellent introduction to all of these topics. It is really thefirsttoattemptsuchasynthesisandprovidesavaluablecompendiumofinfor- mation on black holes for students of all ages and researchers of all flavors. The collection of problems at the end of each chapter encourages enthusiasts to gain a mastery of the subject and undoubtedly will help lead to much-needed further insights into one of the biggest mysteries in fundamental physics today. London, England Malcolm Perry Preface Black holes are predictions of Albert Einstein’s theory of general relativity and have been the focus of intense studies for over a century, as they provide a rich source of theoretical and experimental challenges. Black holes entail some of the deepestpuzzlesontheroadtowardquantumgravityandengenderedseminaltheo- reticaldiscoveries,suchasthermodynamicalpropertiesofblackholes,theirrolein theholographicprinciple,andtherecentmergerofgeometricalandquantuminfor- mation concepts. Black holes, by their very definition, are hard to detect directly. Recenttechnologicaladvancementshaveledtonovelmethodsofdetectionthrough gravitationalwavesandbyobservingtheirshadows.The2020physicsNobelprize awarded “for the discovery that black hole formation is a robust prediction of the general theory of relativity” is a testimony of the importance of black holes. In this book, we elucidate the theoretical concepts of black hole physics and discusssomeofthemainphenomenologicalsignaturesandprospectsinrecentand future black hole observations. The scope is narrow in the sense that everything we present is in one way or another related to black holes; at the same time, our scope is ambitiously broad, since we cover ground including observational challenges, geometrical tools, thermodynamics, particle creation, holography, and quantuminformation.Theprincipalgoalofthisbookistoprovidethereaderwith an up-to-date status of black hole physics. This book is mainly intended for three groups: 1. graduate-level physics students who intend to start their research career in the field of black holes; 2. postdocs who recently changed their research focus toward black holes and want to get up-to-date on recent and current research topics; 3. advanced researchers who want to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. The main style we pursue is hands-on, which in particular means that there will be numerous exercises as an integral part of the learning experience conveyed by our book. We assume the reader is familiar with the basics of general relativity and with standard undergraduate physics, like special relativity, thermodynamics, quantum mechanics, and statistical mechanics. Moreover, we assume familiarity with the basics of quantum field theory on Minkowski space. Apart from these, ix x Preface we have tried to cover the required material in the main text accompanied by appendices. We mainly focus on established knowledge, but also give a taste of current trends and issues of dispute. Since the research field of black holes is a rapidly advancing area on theoretical, numerical, and observational fronts, topics that are only partially addressed and understood by the time of publication of this book may well become a part of established physics in just a few years. Wecoveralltopicsandareasthatweconsideressentialsofblackholephysics. However,asalwaysthereareseveralinclusionsandexclusionsoftopicsthatsome readers may find questionable. While our choices naturally are influenced by our field of research, theoretical aspects of black holes, we aspire to give a broad and fair overview of all aspects of black hole physics. We have strived to 1. make this a self-contained book on black holes, 2. cover basic, advanced, and expert topics suitable for a 1-year course, 3. provide many exercises and (hints for) solutions, and 4. guide the reader through current research topics. Whilecoveringawiderangeoftopics,weavoidbeingoverlyencyclopedic;wedo not intend to give a full literature review on all topics and discuss only the most essential points. At the end of each chapter, we provide suggestions for further reading. Finally and importantly, each chapter comes with a set of problems that are an integral part of the book. There are two types of problems: (1) Exercises meant to engage the reader with the analysis and discussions of the chapter by filling in the gaps of calculations and proofs. (2) Problems that are extensions of the analysis of the chapter. They are interesting and relevant, but we did not find them crucial enough to be added to the main text. How to Read and Use This Book Weprovidenowaroughguidelineforhowtousethisbook.Graduatestudentswho readthisbookontheirownshouldattempttosolveatleasthalfoftheexercisesat the end of each chapter, as a cross-check whether they have digested the material in the main text. If you are such a student and have already some experience with blackholes,youmayskipreadingsomeoftheearlierchapters,butyoushouldstill try to complete the exercises just to make sure that you know what you thought you knew. If you have no experience with black holes whatsoever, then just start reading Chap. 1 and proceed from there. Postdocs reading this book may want to skip ahead to their main focus of interest, which is likely to be in the second half of the book, Chaps. 6–10. Still, we recommend that you have a look at some of the exercises in the first five chapters. Essentially, the same is true for more advanced researchers who want to learn about advanced aspects of black hole physics. If you plan to use this book as a tool for teaching, then our main recommen- dation is to drop stuff that you find less relevant and to schedule at least one year