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Chapter 3 Characterizing black holes（第1页）

Chapter3Charagblackholes

InChapter1，weiheasssingularity，fravitationalcollapse，andsurroundedbyahorizon。ExamplesofsuchobjectsthatarenotspinningarecalledSchwarzschildblackholesandthistermspecifiotesblackholesthataren:inthejargon，theyhavenospin。Simplyput，theonlycharacteristicthatdistinguishesoneSchwarzschildblaaherthanlo）ishowmassiveitis。InChapter7wewilllearnhowblackholesgrowbutfornow，itwillsuffioseuyisthekeyihereisanyrotatiohepre-atter，hehecollapseoccurstherotationratewillinlesssomethingactstostopthathappening）。Thisarisesduetoaremarkablephysiownastheservationofangularmomentum。Thislawisillustratedbyapirouettingskater:asshepullsherarmsinshespihesameway，ifthestarthatgivesrisetotheblackholeisgentlyrotatiheblackholethatitultimatelyformswillbespinningsignifidistermedaKerrblaoststarsareinfag，becausetheythemselvesarefravitationalcollapseofslmassivegasclouds。（Ifsuchagascloudhadeveofiohegcloudwillhavenularmomentum，aeroinglysmallervolumethefinalrotationofthecollapsedobjectmayid。）Thusweseethatrotation，moreonlycalledspiobeaprevalent，ifnotactuallyaubiquitous，characteristicforblackholesthathavejustformedfromtheatter。Wespinisasiableirophysicalblackholesasitisi-daypolitics（thoughiercaseitarisesfromsomethiheservationofangularmomentum!）。

Wehaveasedphysicalparameter，thatularmomentum，isacharacteristicthatdistinguishesoneblaaasmassdoes。Thus，therearetwopropertiesofblackholesthatareimportanttokeepinmihebehaviourofblaassandspin。Inprihirdcharacteristicofblackholesthatmightberelevanttotheirbehaviour:electricalcharge。Thisisalsoaservedquantityinphysidtheforcesbetweericowicforces，haveanumberofresemblaogravitationalforce。Akeysimilarityisthatbothare（escales）examplesofinverse-squarelawsmeaningthat，iwomassiveobjects，asyoudoublethedistaseparatesthemfromohegravitatioheyexperieoaquarterinalvalue。Akeydifferewhilegravityisalwaysattractive，electrostaticchargesareoractive（whewobodiesareoppositelycharged，i。e。oiveaherisheyareatothertimesrepulsive（whenthebodieshaveesighpative，theyrepeleachother）。Iftwedbodieshavethesametypee，theicrepulsioopreventthemg，evenifgravityistendingtoattractthem。Sowhilechargeprihirdpropertyofblackholesthatohopetomeasure，iyachargedblackholewouldberapidlyhesurroundiistherefoodoperationalassumptionthatthereareopropertiesofblackholesthatdistinguishonefromanother:massandspin。That'sall!

Now，youmightwoherblackholescouldbedistiheirighthavebeenformedfrasaheliumgascloud。Whyshoulditbethattheproveheatterthatgaverisetotheblackholeisn'tmahemeasurablepropertiesoftheblackholesubseque'sbeation'tgetoutoftheeventhhtisthemeansbywhiightbetrawehavealreadyseeniitotesihorizonofablackhole。Thusthechemipositiohatfellintotheblackholeoeffethepropertiesoftheblackholeasdetermiheoutside。Itwouldtothinkofgravityassomethiogetoutof'theblackhole。Theuedexistenceofagravitatioernaltotheblaethingthatislaiddowionoftheblackholeasspacetimebeesdistorted。Noinflueniheblackholegetheexterertheeventhorizonhasformed。

Blackholeshavenohair

Wheodesotherperson，adistinguishingcharacteristicthatisofteheirhair（forexample，strawberryblreyorchocolatebrown）。Therearesometimesthenatureofpeople'shairasteortheirnationality。InformationaboutfurtherphysicalcharacteristicssuassIndex'mightprovideinformatio。Intrasttohumans，blackholesareehaveabsolutelynodistinguishingcharacteristicsotherthantheirmassandtheirspiihereasonsnotedabove）。ThisiscapturediphraseBlackholeshavenohair'，edbyJohoemphasizethatthereisnothingaboutablackholethatbearsahesprogenitorstar。Notitsshape，notitslumpislasmagitschemiposition。Nothing。Calsdoneby，amoheBelarusianphysicistYakovZel'dovistratedthatifaarysurfacecollapsedtoformablackhole，itseventhorizonwouldultimatelysettledowntoasmoothequilibriumshapehavingnolumpsorbumpsofanykind。So，ablaeverhasabadhairday!Theonlythingsyouowaboutitareitsmassandspin。

Spiy

&hemostremarkablefeatureofaspinningblackholeisthatthegravitationalfieldpullsobjedtheblackhole'saxisofrotatioowardsitstre。Thiseffectiscalledframedragging。AparticledroppedradiallyontoaKerrblackholewilla-radial（i。e。rotating）posofmotionasitfallsfreelyintheblackhole'sgravitationalfield。

Whatthismeansforatestpartigspin（suchasasmallgyroscope）isthatifitfallsfreelytmassivebody，suchasaKerrblackhole，itwillacquireagetoitsspinaxis。Itisasthoughitslocalframeofreferencewasdraggedbytherotatioralmassivebody。Thisphenomenon，dis1918，calledtheLehirriuallyootjustaroundblackholes，buttosomeextentaroundanyspi。Ifyouputaveryprecisegyrosorbitarouheframedraggihegyroscopetoprecess。

ItisEinstein'sfieldequatiohemathematicsofblackholesand，asalsomentionedinChapter1，KarlSchwarzschildsolvedtheseequationsforthecaseofthestationary（n）blaarkableatgivehisin1915，thesameyearthatEiroducedhisgeheoryofrelativity。ThecaseofthespinningblackholewastreatedmuchlaterbyNewZealanderRoyKerrin1965。Afewyearsafterthis，theAustralianBrandonCarterexploredKerr'ssolutioill。CartercarriedoutahiionintothecesoftheKerrmetric。Heestablishedthataspinningblackholecausesadramatigvortexiimethatsurroundsitwhicharisesbecauseofthereferenceframe。Anexampleofavortexisawhirlwihetreofthewhirlwindtheairsidly，gwithitanythinginitspath，beithayinahayfieldorsa。Furtherfromthewhirlwindtheair（andhencehayorsand）rotatesmuchmoreslowly。Soitistoo，withspacetimesurroundingaspinningblackhole:farawayfromtheeventhorizowhichspacetimeitselfrotatesisslow，butatthehorizoselfspinswiththesamespeedthatthehorizonspins。

&horizonforthespinning（Kerr）blauchthesameasforanon-spinning（Schwarzschild）blackhole，exceptthatthefastertheblackholeisspihegravitatioialwell:aKerrblasadeepergravitatioialwellthanaSchwarzschildblaemass，andthereforeaKerrblackholebeamysouranon-spitowhichwereturnihemeaishelpfultosummarizethisbehaviourbysayihorizonofaSchwarzschildblackholedependsonlyonmass，butthatofaKerrblackholedependsonbothmassandspin。

Anoutstaioherecouldbe，eveninprinyspagularitiesthatarenotehinandhiddehorizons-aso-akedsingularity'。Bydefinition，allblackholesolutioeiiohorizonsand，asshoter1，nolightandthereforenoinformationeswithinsus。Allblackholesingularitiesarebelievedtobeehihorizonsanaked'，sothatdireationaboutthesingularityisinaccessiblefromtherestoftheUheso-isorshipjecturewasformulatedbytheBritishmathematiRogerPeesthatallspagularitiesfularinitialsarehiddehorizonsandthattherearenonakedsiinspace。

Howmuistoomuch?

Thereisalimittohowmugularmomentumablackholehave。Thislimitdependsonthemassoftheblackhole，sothatamoremassiveblackholefasterthanalessmassiveblackhole。AblackholethatisrotatihismaximumlimitisknowremeKerrblackhole。ItispossibletoshowthatifyoutrytospinupablaakearemeKerrblackhole，byfiringrapidlyrotati（i。e。givingitastir）therifugalfortthematterfromeveheeventhorizon。

&heroutfromtheeventhorizblackholeisannifitmathematicalsurfacewhiowiclimit。Thedraggiialframesmeansthatifthespinofthemassivebodyisherearenostationaryobserversihissurface:everyphysicallyrealizablereferehestaticlimitmustrotate。Withinthissurface，spaningsofastthatlightitselfhastorotatewiththeblackhole，i。e。itisimpossibletoremaiheregioatidtheeventhorizonisknownastheergosphere，whichratherglyisnotspherical，asshowninFigure10。Iorialdirestheergosphereismuchlargerthahorizon，butinthepolardirestheradiusosphereisthesameastheradiusoftheeventhorizshapeosphereisanoblatesphertheshapeofaJarrahdalepumpkin（withoutthestalk）。Thefirsttwosyllablesosphere，however，theGreekntowork&#y'（asinergonomiwhichtheolduheerg，isalsoderived。Itisintriguiinadditireekverbergowhistoendkeepariatelyfortheheergosphere。PerhapsthismayhavebeeninthemindserPenroseariosChristodoulouwhodedthehisregionaroundaspinningblackhole。Theimportaheergosphereisthatitistheregionwithinwhiergybeextractedawayfromtheblackhole。

10。ThedifferentsurfadaSchwarzschild（stationary）bladaroundaKerr（spinning）blackhole（ilyusedrepresentationofBoyer-Lindquist'ates）。

&heergospherespaning，partiatteracealsogetsweptupintoarotationalmotioatiyisthereforestoredinthisrotationofspace，averyimportantpointtowhichwereturninChapter8。

Whiteholesandwormholes

&eiioivityareparticularlyridallowmaialternativeversionsofcurvedspacetime。Thisprovidesanalmostiiblesourceofpossibleuniversesfiststodesdthinkabout。Whichtypeofuuallyliveinisamatterthatlybedecidedbyobservation（ifatall!）。Butthatdoesn'tstopmathematicalphysicistsplayingaroueiionstofindallkindssolutions。

&riguibedreamtupbymathematicalphysicistsiswhatiscalledawhitehole。Awhiteholebehavesjustlikeablackholebutwiththedireereversed（imagineamovieplayedbackwards）。Iterbeiisspewedout。Iheeventhionfromwhistakesionintowhigcouldevereerexitsfromawhitehole，iteverreturirefutureisoutside。AsweseeinChapter6，ablackholeisformedfromagstarauallyevaporatebythelawsofquantummetoHawkingradiatioer5）。Awhitehole，oherhand，lyresultfromradiationthatforsomereasonspontaneouslyassemblesintoablackhole。ItisouandhowthiscouldhappeninpradmlasEardleyhasdemowhiteholesareiable。

&einandhisstudentNathanRaroueiioheyfouingsolutiioimecouldbestromightbepossibleforittobeesuffitlyfoldedthattacetimereviouslybeeedbyalargedistaneectedbyasmallbridge，orwormhole，asshowniheenormousdistaarsandgalaxieshavealwaysbeenunfavourableforthoseishtosethumandramasonaidwormholes（alsokein-Res）haveprovidedtheperfegdeviceforwriterstotransporttheirheroesandvillainsabout。Thismathematitionhasbeenaothewritersofs，becauseitprovidesareadymeansfenormousdistahroughspadtherebytosustainvarioushighlyartifidunbelievableplotdevices。Yetagain，wehaveiowormholesactuallyexistinourUniverse。Inaddition，thereissiderabletheoreticethatawormhole，oned，wouldablef。Itseemsthattokeepawormholeproppedopen，oneneedsalargeamouiveeer，andallnormalmatterhaspositiveehisisectedwiththefactthatgravityisnormallyalwaysattraatterpassingthroughawormholemaybeenoughtodestabilizea，gittoturnintoablackholesingularity。

11。Awormholegtwootherwiseseparateregioime。

Ifwormholesdidexist，andaintainedforanyreasoime，theywouldhavesaies。Notonlywouldtheyprovideameansfanenormousshortcutacrossavastexpanseofspace，buttheywouldalsoallowatravellertojourneybatime。Oherue-likecurves，loopsiimeinwhichthelightaring（seeFigure12）sothat，likeinthemDay，apersaloime-likeplyrepeattheirsameexperiencesoverandain。

Infact，thereareanumberofsolutioeiionsinadditiontowormholeswhichhavethisalarmingaiveproperty。In1949，themathematiKurtG?elfoundasolutionthatdescribedaspinninguhissexactlythesamesortofe-likecurveswhichpassthrougheventsagainandagaininanendlessGroundhogDaycycle。（Evidentlyfreewill'isnotpartofthefieldequatiooftheKerrsolutionthoughttohavegenuinephysiifitherealworldisthatwhichdescribesthespacetimeoutsideoftheeventhorizoisuhepartoftheKerrsolutioheeventhorizoid，hasanyphysicalrelevahispartoftheKerrsolution，thesingularityisnotapoint（asitisforthenblackhole）buthastheformofarapidlyr（however，thephysicalvalidityisveryspeculative）。Thisring-likesingularityissurroundedbye-likesuchacurve，yourfutureisalsoinyourpastandyouhavethetheoreticalpossibilityonerasbeforetheyhadproducedyourparents!Thustheexistene-likecurvesseemstocreatethepossibilityofallkindsofparadtotimetravel。Onepossiblesolutiontothisistoadmitthatwedoheorythatlinksquantummeics（whichdescribestheverysmall）aivity（whichdescribestheverymassive），inotherwordsatheoryofquantumgravity。Wedon'tknowthephysielymassivebutverysmallobjects。MostphysikweofullyuhebehaviourofspacetimeveryclosetosihusitmaybethatthesestraioeiionsdonotactuallyotheUheyareprohibitedbyitsfualquantummeature。Quasmay，forexample，destabilizewormholes。StephenHawkiobethedhascalledthispriheologyProtejecture'。HehasquippedthatthisistheunderlyingprikeepstheUniversesafeforhistorians。

12。Ae-likeloop，onwhichyourfuturebeesyourpast。

Thereismuchabouttheinteriblackholesthatpushesoffualphysiitsaowheremuchofourdesishighlyspeculative。Bytrast，therotationofblackholesaontheirsurroundingsissomethingthathasenormouspractiifiderstandingwhatweseewithourtelescopes。Thusourosiderihappenstomatterwhenitfallsintoablackhole。