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Chapter 1 What is a black hole（第1页）

Chapter1Whatisablackhole?

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Ablackhiohefravityissthatnothi，travelfastenoughtoesitsihoughtheywerefirstthefertileimaginatioicalphysicists，blackholeshaveifiedintheUheirhundredsandatedforintheirmillions.Althoughiheseobjeteractwith，andthusiheirsurroundingsinawaythatbehighlydetectable.Exactlywhattheiionisdependsonproximityrelativetotheblackhole:toodthereisfurtherafieldsomedramatidspectaomena>

&ermblackhole'wasfirstmentionedinprintinanartiEwingiingonasymposiumheldinTexasin1963，althoughsheionedwhoedtheexpression.In1967，AmeriphysiWheelerhandfravitationallypletelycollapsedstar'aopopularizetheterm，thoughtheceptofacollapsedstaredbyfellowAmerisRobertOppenheimerandHartlandSnyderba1939.Infact，themathematidationsofthemodernpictureofblackholesbeganratherearlierin1915，hysicistKarlSchwarzseimportaioein's（knownasthefieldequationsiheoryofRelativity）fortheisolatednmassinspace.

TwodecadeslaterintheUK，alittlebeforeOppenheimerandSnyder'swork，SirArthurEddingtonhadworkedoutsomeoftherelevaithetextofiingworkbytheIndianphysicistSubrahmanyandrasekharonenstostarswhehephysicalimplisofEddington'selytheassivestarswhentheyhaveusedupalltheirfueltoformblackholes，EddingtonhimselfproheRoyalAstronomicalSo1935asbeing‘absurd'.Despitetheapparentabsurdityofthenotion，blackholesareverymuchpartofphysicalrealitythroughalaxyandacrosstheUheradvancesweremadeiedStatesbyDavidFieinin1958，whoestablishedtheexistene-waysurfadingablackholewhosesigweshallstudyintheingchaptersisimmeehissurfa'tallowlightitselftobreakfreefromthepravitationalattrawithinandisthereasonwhyablackholeisblack.Tobegiandhowthisbehavihtariseweofirstuandaprofouhephysicalworld:thereisamaximumspeedatartiyobjetravel.

Howfastisfast?

Alawofthejuifyouwanttoescapeapredatoryouorunfast.Unlessyouhaveexalouflage，youwillonlysurviveifyouareswift.Themaximumspeedwithwhichamammalespleasantsituationdependsonplexbiochemicalrelatioweenmass，musgth，aabolism.ThemaximumspeedwithwhichthemostrapidlytravelliyintheUravelisthatexhibitedbyparticlesthathavenomassatall，suchasparticlesoflight（knohotons）.Thismaximumspeedbegivenverypreciselyas299，792，458metrespersed，equivalentto186，282milespersed，roagamillioerthanthespeedofsoundinair.IfIcouldtravelatthespeedoflight，Iwouldbeabletotravel

frommyhomeioAustraliaieenthofased，barelytimetoblink.LighttravellingfromourheSueightmiraveltous.Fromouroutermostpla'sajourafewhoursforaphototheSulight-minutesawayfromEarthau-hoursawayfromus.ThishastheiihatiftheSunstoppedshiningorifuurnedpurple，hdoutaboutsuchimportantinformatihtminutesorafewhoursrespectively.

&'snowsiderhowfastlighttravelfromevenmoreimmeantpointsioEarth.TheMilkyWay，theGalaxyinwhichourSolarSystemresides，isafewhuhousandlight-yearsacross.ThismeansthatlighttakesafewhuhousaravelfromoheGalaxytotheother.TheForheerofgalaxiestothelalaxies（ofwhichtheMilkyWayisasignifitmember）andishundredsofmillionsoflight-yearsawayfromus.Thus，anobserveroingastarinagalaxywithintheFornaxclusterlookingbackthtnowmight，ifequippedriateiion，seedinosaurslumberingarouh.However，itisonlythemind-boggliheUmakesthemotionoflightlooksluggishandtime-ing.Theroleofthespeedoflightasamandatoryupperlimithasanintriguiwheosiderhowtolauospace.

Escapevelocity

NowsupposesomedisasteroccurswiththeresultthattheentiremassoftheEarthwereshrunktoapoint，havingnospatialextentwhatsoever.Wecallsuobjegularity.Ithasmass'，amassiveobjectthatoccupieszerovolumeofspace.Ataverysmalldistanetreawayfromthissingularity，theescapevelouchlargerthanitwasat1，600km（andinfactwouldbeabout10%ofthespeedoflight）.Closertothesingularitystill，justureawaytheescapevelocitywouldbeequaltothespeedoflight.Atthisdistaitselfwouldnothavesuffitspeedtoescapethisgravitationalpull.Thisisthekeyideatouandhowblackholeswork.

Itiswuseularity'.Wedoattheendpointofaggravitationalcollapsethemattergoesdowritbutratherthatourclassicaltheravitybreaksdoweraquantumregime.Fromhereon，wewillusethetermsingularitytorefertothisultra-dee.

&horizon

Nowimagironautflyiandthatyouareapproagthissingularity.Whilestillatsomedista，youcouldalwaysthrioreverseafromit.Buttheclet，theharderadigbees.Eventuallyyoureachadistanwhichitisimpossibletoesatterhowpowerfulyihisisbecauseyouhavereachedtheeventhorizoically-definedsphericalsurface，whichisdefiheboundaryinsideofwhichtheescapevelocitywouldexceedthespeedoflight.Fht-experimehcollapsedtoapoint，thissurfacehereofradiusorewiththesingularityatitstre，easyenoughperhapsforourspacecrafttoavoid.However，theeventhorizonbeuchlargerwhentheblackholeisformedfromacollapsedstarratherthanacollapsedplahorizonhasanimportantphysisequence:ifyouareonthatsurfasideit，thelawsofphysicssimplywon'tallowyoutoescapebecausetodosoyouwouldobreaktheuniversalspeedlimit.Theeventhorizonisamandatorylevelofdemar:outsideityouhavefreedomtodetermii，andyourfutureremainsunalterablylockedwithin.

TheradiusofthissphericalsurfaamedinhonourofKarlSchwarzsentionedearlier.WhileasoldierinWorldWarI，Schwarzschildprovidedthefirstexactsolutioein'sfamousfieldequationsthatunderpiivity.TheSchwarzschildradiusiswrittenasRS=2GMc2whereMisthemassoftheblackhole，Gison'sgravitationalt，andcisthespeedoflight.Usingthisformula，theSchwarzschildradiusoftheEarthesouttobejusture.Similarly，theSchwarzschildradiusoftheSunisfoundtobe3km，meaningthatifthemassofourSuncouldallbesquashedintoasingularity，thenatjust3kmawayfromthispointtheescapevelocitywouldbeequaltothespeedoflight.AblaebilliontimesmoremassivethantheSun（i.e.havingamassof109solarmasses）wouldhaveaSchwarzschildradiusonebilliontimeslarger（theSchwarzschildradiusofapointmassthatisnsimplyscalesdirectlywithitsmass）.AsIdesChapter6，suchmammothblackholesarebelievedtobeattheanygalaxies.

Thisdesoftheeventhorizonbereasonablythoughtofwithionianphysideed，physititiesresemblingblackhiuriesbeforeEihersprofoundlygedofspadtime.Theprinkerswhoimagineddarkstars'thatresembleblackholeswereJohnMidPierre-Simoingbathe18thtury，andIwillnowexplainwhattheydid.

&heremarkablethingsaboutastronomyishowmudiscoverabouttheUniverseevenwheuetEarth.Forexample，nohumanbeiedtheSuhepreseheSuhelate19thturybyanalysirumofsunlight.Thisisparticularlyremarkableasthisstitutedthediscoveryoftheelemeself;itwasfoundontheSunldeteEarth.Evehe18thtury，someoftheideasbehindblackhined，andinparticulartheideaofwhatiscalledadarkstar.Thepersohefirstimaginativeleapwasverymuchaprodue.

JohnMichell

TheGeianerawas，inEnglaivepeaglishCivilWarwaslo，andEnglandhadbeealaivedomestiquillity（theriseofNapoleoillsomewayoff）.Likehisfatherbeforehim，theReverendJohnMichell（Figure1）receivedauyedudeheChurgland.AsareThorYorkshire，Michellwasabletouehisstificresearch，followinguphisisingeology，magism，gravity，light，andastronomy.Inonwithotherstistswithetime，suchastheastronomerWilliamHersdthephysirydish（ersonalfriend），Michellwasabletoridethewaveofthehinking.SirIsaahadrevolutiohewayinwhiiverseerulatinghislawofgravitationwhiedtheorbitsoftheplaheSolarSystemasbeihesameforcethatcausedhisfamousappletodropfromthetree.

1.JohnMiath.

&onianideasallowedtheUudiedusiidthisfreshbreedofstistswasabletodeploythisnovelworld-viewifields.Michellarticularlyedtousehihedistaarsbyusisofthelighttheyemitted.Hecameupwithvariousschemestodothis，byrelatingastar&#htscolour;healsosideredbinarystars（pairsravitationallybouher）aalmotionscouldgiveusefuldynamiichellalsoiarstendtoparticularareasofthesky，testingthisagainstarandomdistributionandinferringgravitationalg.heseideasracticableatthetime:fewbinarystarswereknown（thoughHerschelrodupressivecataloguesofvariousdoublestarsas）aioweenastar&#htscolourturobenotquiteasMichellhadthoughtitwas.heless，MichellwasstrainingtodoforthewiderUoheSolarSystem:allowastifial，anddynamialysisofobservationstoprovidenewinformationabouttheproperties，masses，anddistaheheavenlybodies.

&isightthatichellfollowedfromtheideathatparticlesoflightare，inMichell'swords，attrathesamemannerasallotherbodieseareated;thatis，byfthesameproportiontotheirvisiiae[bywhitmass]，ofwhichthereoreaso，gravitationbeing，asfarasweknow，orhaveaobelieve，anuniversallawofnature'.Suchparticlesemittedfrestarwould，hereasoned，besloweddowionalattraofthestar.ThusthestarlightreagEarthwouldbeslower.onhadshownthatlightslowsdowninglass，andthisexplaiheprincipleofrefra.Ifstarlightwasindeedsimilarlyslowed，Michellarguedthatitmightbepossibletodetectthisslowingbyexaminingstarlightthroughaprism.Theexperimentwastried，notbyMichell，butbytheAstronomerRoyal，theReverendDrNevilMaskelyne，wholookedforthediminishiabilityht.dishwrotetoMithatithadn'tworkedandthatthereisnotmuchlikelyhood[sidinganystarswhoselightissensiblydiminished'.Michellwasdismayed，butsuicalspesrequiredmugofimpoarlightaffectedbythegravitationalattraofthestarfromwhichitisemitted?Michell'tbesure.Buthewasboldenoughtomakeaiion.

Ifastarwassuffitlymassive，andgravityreallydidaffectstarlight，theionalforcecouldbesuffittoholdbacktheparticlesoflightpletelyahemfromleaving.Suobjectwouldbeadarkstar.Thislittle-kingioryinYorkshirehadthusbeepersontoceiveofablackhole.However，sofarMichell'srammethedistaarslayiwasmore，hishealthhadbeeandthishadstoppedhimusinghistelescope.dishwrotetohimagletter:ifyourhealthdoesnotallowyoutogooelesayatleastpermittheeasierandlesslaboriousemploymeheworld.'Thissingularexampleofajokefromdish（whowasnotoriouslybuttooaMichellhadceived.Weighingtheworld'meainwhichtweleadspheresateitherendofthebeamofatorsioractedbytwostationaryleadspheres.ThisallowsohestrengthofthegravitatioherebyioftheEarth.Noohisbefore.Michell'sideawasbrilliant，buthedidn'tlivetopletetheprojestead，Michell'sexperimenterformedbydishandisnowknownasdish'sexperiment.Thistransferofcredittodishismorethaedforbythenumerhsmadebydishwhieglectedtopublishatributedtosubsequentresear's'lawandb's'law）.

Pierre-SimonLaplace

OhersideoftheEnglishel，Pierre-SimoeranquilidyllaffordedbythepeacefulperiodoftheEe.LaplacelivedthroughtheFreion，thoughhiscareerprosperedasheihenewlyfouutdeFrahe恈olePolyteique.HeeveaperiodasMiheInteriorunderNapoleon，ashort-livedappoiheEmperorcametret.NapoleoLaplacewasafirst-ratemathematibutasanadministratorhewasworsethanaverage.erwroteofLaplacethathesoughtsubtletieseverywhere，lyproblems，andfinallycarriedthespiritof"infinitesimals"iration'.heradministratorsto，buttheworldhashadfewmathematisasprodudinsightfulasLaplace.Hemadepivotaltributiory，probability，mathematics，celestialmeiy，andphysics.Heworkedontopicsasdiverseascapillaryaets，inductivereasoning，solarsystemstability，thespeedofsouialequations，andspheriieoftheideashesideredwasdarkstars.

In1796LaplacepublishedhisExpositiondusystèmedumoeedpublic，thisbookdescribesthephysiwhiyisbased，thelawofgravityaiosintheSolarSystem，andthelawsofmotionandmeics.Theseideasareappliedtovariousphenomena，ingthetidesandthepreoftheequihebookalsosLaplace'sspesinoftheSolarSystem.Oicularpassageisofspecialrelevaoourstory.Laplacemadeacaleah-likebodywoulditsescapevelocitywasequaltothatoflight.Heshowed，quitecorrectly，thatthegravitatithonthesurfaceofastar，withdensityparabletothatofEarthbutwithadiameterofabout250timesthatoftheSun，wouldbesoievenlightwouldbeabletoescape.Thus，hereasobodiesintheUhereforebeiheystillbelurkiableinthedarknightsky，whileweimagiheonlythingsoutthere'werethebrightlumiwesee?TheHungarianastronomerFranzXavervohatLaplaceprovidethecalsthatledtothis，andLaplacethisup（inGermahejournalsthatvoed.

Holacewasbeihewavetheht.BothMichell'sandLaplace'sideasartonthecorpusculartheht.Iflightweretosistoftinypartiitseemedreasoheseparticleswouldbeaffectedbyagravitationalfieldandwouldbebouarofsuffitsize.Buttheearly19thturysawanumberofexperimentswhichseemedtogivegreatercetothewavetheht.Iflightwereinsteadawave，thenitwashardertoseethatitshouldbeaffectedbygravity.Laplace'sdarkstarprediwasquietlyomittedfromlatereditioiondusystèmedumoerall，MidLaplacehadbeeuringandexpltheory，ratherthanbeiheoexplaiionsandthus，thisideawasfottenforawhile.TheobjeedbyMidLaplacewerethusdarkstars'，enormousobjetheUniversewhichbyvirtueoftheirmasscouldsustaiemsbutbyvirtueofthissamebulkotbeobservedviatheradiationoflight.Starlightemittedfromthesurfaichell'sandLaplace'sdarkstarswouldbetoosluggishtooveretheintensesurfacegravity.WhatMidLaplaothaveguessedwasthatsutuanaasswouldbeuooreover，intheircollapsetheywouldpuheveryfabricofspadtimeaoasingularity.Thusblackholes'arenotdarkstars'aheargumentfihtheastronomicaldiscoveryofblackholeswewillfirstouhenatureofspacetime.

&ime

OureverydayexperienceleavesusfortablewiththenotioangibleUniversemaybedescribedbyoemporal（ortime）atetaialates（forexamplex，y，andzalouallyperpendicularaxes，astrutedbyReesandknownasates）.IeinpublishedhisrevolutionarypaperonSpecialRelativity，therelativityofmotionandstationarity.In1907，HermannMinkotheseresultscouldbeuoodmoredeeplybygafour-dimensioimewhosepoints，speowbythe4-Date（t，x，y，z），dto‘events'.Aissomethingthathappensataparticulartime（t）andataparticularplace（x，y，z）.Such4-DatesinwhatisknownasMinkoecifyexactlywhereandwheostein'sspecialtheoryofrelativitycouldbeformulatedintermsofMinkowski'sspadprovidesatdesofphysicalprodifferentframesofreferemoverelativetooher.Aframeofreference'issimplytheperspectivepossessedbyaparticularobserver.Einsteiheoryspecial'becauseitdealsonlyarticularamelyrefereareiialframesofreferehespecialtheorylybeappliedtouniformlymoving，ed，framesofreference.Ifyoudropastoround.TheframeofrefereachedtothestoneisaingframeofreferenedbyEinstein'sspecialtheory.Whereyouhavegravity，youhaveac.

ThisdratedEioformulateageheoryofrelativity，whichhepublishedadecadeafterhisspecialtheory.Whathefoundwasthatwhereasspakowskispacetimewererigidframeworksinwhichobjectslive，moveaheirbeing'，spacetimewasactuallyamorerespocouldbedotherwisedeformedbythepresenass.Oncemassispresentinaphysicalsituatiohefollowirikedbehaviourdescribesreality，lysummarizedbyJohnWheeler:

·massaspacetime，tellingithowtocurve！

·spacetimeaass，tellingithowtomove

ThisbehaviourisquantifiedbyEinstein'sfieldequationswithiivity，whichrelatethecurvatureofspacetimetothegravitationalfield.

Physiciststalkaboutagravitatioialwellassurroundingamassiveobject.TheshowninFigure2ehespacetimeisdistortediyofacoupleofblackholes，whereeaberegardedasawaywhichisdirectlyrelatedtoitsmassahegravitatioself.Thesingularityiimemayberegardedaswherethecurvatureiimebeesveryhighandyougobeyondtheclassicaltheravity，iumregime.Theevenththesingularityfunsasaone-

2.Thedistortioure，iimeduetothepresenasses.

membraidphotoheblaoutsidebutnothingeswithinthehorizonoftheblackholeouttotheexternalUmassisnottheoablaaypossessandbemeasuredby.Iftheblackh，thatistosayitpossessessomespin，theneveremebehavies.Beforeweexamiakealittledetourtolearnalittlemoreabouthowwemayschematicallyrepreseself.