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Chapter 3 Characterizing black holes（第1页）

Chapter3Charagblackholes

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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.