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Chapter3Charagblackholes
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InChapter1，weiheasssingularity，fravitationalcollapse，andsurroundedbyahorizon.ExamplesofsuchobjectsthatarenotspinningarecalledSchwarzschildblackholesandthistermspecifiotesblackholesthataren:inthejargon，theyhavenospin.Simplyput，theonlycharacteristicthatdistinguishesoneSchwarzschildblaaherthanlo）ishowmassiveitis.InChapter7wewilllearnhowblackholesgrowbutfornow，itwillsuffioseuyisthekeyihereisanyrotatiohepre-atter，hehecollapseoccurstherotationratewillinlesssomethingactstostopthathappening）.ThisarisesduetoaremarkablephysiownastheservationofangularmomentuThislawisillustratedbyapirouettingskater: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，evenifgravityistendingtoattracttheSowhilechargeprihirdpropertyofblackholesthatohopetomeasure，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.
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