Introduction to Black Hole Physics PDF
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Introduction to Black Hole Physics This page intentionally left blank Introduction to Black Hole Physics Valeri P. Frolov & Andrei Zelnikov University of Alberta 1 3 GreatClarendonStreet,OxfordOX26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork (cid:2)c ValeriP.FrolovandAndreiZelnikov2011 Themoralrightsoftheauthorshavebeenasserted DatabaserightOxfordUniversityPress(maker) Firstpublished2011 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable TypesetbySPIPublisherServices,Pondicherry,India PrintedinGreatBritain onacid-freepaperby CPIAntonyRowe,Chippenham,Wiltshire ISBN 978–0–19–969229–3 1 3 5 7 9 10 8 6 4 2 ToWernerandIngeIsrael withourdeepgratitudeandadmiration This page intentionally left blank Preface This book is about black holes, one of the most intriguing problems of modern theoretical PhysicsandAstrophysics.Itisintendedtoprovideathoroughintroductiontothisareaandto serveasatextforgraduatestudents,postdocs,andyoungresearches. The book is based on the lectures that during 30 years one of the authors (V.F.) has beenreadingatdifferentuniversities.In1981–1992hegavelecturesongeneralrelativityfor studentsoftheMoscowInstituteofPhysicsandTechnology,chairofproblemsofPhysicsand Astrophysics.ThefounderandtheheadofthechairwasacademicianVitalyGinzburg.This wasaone-yearcourse,andhalfofitwasdevotedtoblackholes.Startingfrom1993hehasread ‘Blackholephysics’asaone-termcoursePHYS696,forthePhDstudentsattheUniversity of Alberta. It is natural that during this long time the content of the course has changed considerably,however,itsstructureremainedpracticallythesame.Thisbookisbasedonthe lecture notes for this course and reflects its structure. The main part of the book (presented in Chapters 1–8) follows the lectures. This provides one with material sufficient for a one- term self-consistent course on black holes. The book also contains an additional material, e.g. concerning higher-dimensional gravity, black holes and extra dimensions, hidden sym- metries,wormholesand‘timemachines’,whichcanbeusedfortermpapersrelatedwiththe course(Chapters9and10andAppendices). Ittookusmorethanayeartotransformthelecturenotesintothebook.Duringthiswork we tried to include answers to many questions often asked by students. We included many assignmentsthatmayhelptounderstandthematerialbetter.Mostoftheproblemsaregiven withtheirsolutions.Weusesmalllettertextforthismaterial.Thesamesmalllettertextisalso usedforremarks,which contain examples illustratingthesubject,orbriefnotes onpossible generalizations.Thebookisrichwithillustrations.Inourexperienceproperillustrationsare extremelyhelpfulforbetterunderstandingofthephysicalandmathematicalideas.Wefollow theadviceofSynge(1959):“Itisamistaketoeconomizeinrelativisticdiagrams.Theyform the bridge across which can pass those astronomers whose minds work in the great Greek tradition.” The history of black holes is quite dramatic. The black hole paradigm is based on the Einstein theory of general relativity. During many years theoreticians studied black hole solutions of the gravity equations, but until the beginning of the 1970s the ‘astrophysical community’ ingeneralhadaquitereluctantattitudetotheseideas.Onlyafterthediscovery ofpulsarsandthefirstmissionsofthespace-basedX-raytelescopes,didthisattitudeslowly changeandwarmup.Now,40yearslater,wecannotimagineourworldwithoutblackholes. Theybecameanimportantelementofthe‘bigpicture’ofourUniverse.Therearemoreand morepiecesofevidencethattheirroleintheuniverseevolutionmightbenotonlyimportant butdecisive. viii Preface For many years black holes have been considered as an interesting pure theoretical construction of general relativity with a number of amusing mathematical properties. Now, after the discovery of black holes, the Einstein gravity became an important tool for their study. Collection of data on the properties of the matter in strong gravitational field in the vicinityofblackholeswillalsoprobethevalidityoftheEinsteintheoryitselfinthestrong- field regime. Recently, black holes have been widely discussed in connection with many fundamental problems of theoretical physics. It is worth also mentioning recent interest in the higher-dimensional gravity discussing the possibility of black hole creation in particle colliders. Inthisbookwetriedtopresentthetheoryofblackholesintheformthatmightbeuseful forstudentsandyoungscientistswhoareinterestedinthisarea.Ourbookcombinesphysical, mathematical, and astrophysical aspects of the black hole problem. This is a self-contained textbook, which covers both the most important established results and the most recent new developments.Thebookincludespedagogicallypresented‘standard’materialonblackholes and it also contains relatively new subjects such as the role of hidden symmetries in black holephysicsandblackholesinspacetimeswithlargeextradimensions.Weaddressthebook tothosewhowouldliketostudyblackholephysicsanditsapplications. Thename‘blackholes’,inventedbyJohnWheelerin1967,hasnowbecomeverypopular. Thisisnotonlybecauseoftheirastrophysicalimportance,butalsobecauseblackholesplay theroleofgatesfromourworld,withknownphysics,toaninteriorabyss,wherenewphysics willbecomeimportant.ThisPlanckian-scalephysicsistheHolyGrailoftheoreticalphysics. Quantum gravity and string theory are the first attempts to understand it. Black holes, and also connected with them such subjects as wormholes and time machines, are now almost compulsoryfeaturesofmostsciencefictionbooks. ToillustratehowpopularisthenotionoftheblackholewemadeabriefsearchonGoggle. Thename‘blackhole’hasabout11,800,000results,whileforexample‘neutronstar’isusedin about3,120,000documents.Evenifweexcludesuchthingsas,e.g.,‘blackholesineconomy’, onecanconcludethatatleastinthevirtualrealityblackholesplayanimportantroleandare more‘popular’thansay‘neutronstars’. Therearemanynicepopularbooksonblackholes.Inthemoreadvancedbooksongeneral relativity this subject is often discussed as one of its applications. The wonderful books “Gravitation”, by Misner, Thorne and Wheeler (1973) , “Gravitation and Cosmology: Prin- ciples and Applications of the General Theory of Relativity” by Weinberg (1972), “General Relativity”,byWald(1984)and“LargeScaleStructure”byHawkingandEllis(1973)arethe mostfamousexamples.Morerecently,therewaspublishedatextbook“Arelativist’stoolkit: themathematicsofblack-holemechanics”byPoisson(2007). Thereexistanumberofmorespecializedbooksthatcoverdifferentaspectsofblackhole physics, for example mathematically oriented monographs like “The Mathematical Theory of Black Holes” by Chandrasekhar (1983), “Black Hole Uniqueness Theorems” by Heusler (1996),or“GravityandStrings”byOrt´ın(2004),whichfocusmainlyonmathematicalaspects ofblackholetheory. In1998oneoftheauthors(V.F.)andNovikovpublishedamonograph “Black hole physics. Basics concepts and new developments”. There are also more recent booksthatareorientedmostlytowardsthegeneralpublicandreflectthecontemporarystate ofblackholesinobservationalastrophysics,e.g.,“TheBlackholeattheCenterofourGalaxy” and“High-EnergyAstrophysics”byMelia(2009).Usually,suchbooksaremostlydescriptive Preface ix anddon’tpaymuchattentiontothemathematicalcomponentoftheEinsteintheory,anddon’t describederivationofmanyimportantresultsfromfirstprinciples. Our book is aimed mainly at students and postdocs with the specialization in physics, mathematics and astrophysics. It will also attract the attention of those who would like to investigate the wonderful ‘Black Hole Land’ on their own, and to become equipped with mathematical tools and ideas that would allow them to find out answers to many of their questions. ValeriP.Frolov AndreiZelnikov Edmonton,February2011
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