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Chapter5Entropyandthermodynamicsofblackholes
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Youarewhatyoueat
Itisoftensaidthatyouarewhatyoueat.Thusifyourdietispurelyjunkfoodandchocolate，thenyourplexion，ionyourphysidmentalwell-being，willberatherdifferentthanifyousubsistohydietofsaladaerraneanfood.However，itseemsthatblackholesarenotfussyeaters.Whethertheyarehupavastexpaerstellardustoracubiclight-years，theirmasswillsimilarlyinexorably.Infact，afterablackholehasfissumptuousmeal，youhavenowayoftellingwhatitwaseating，onlyhowmuchithased（althoughyoucouldtellifwhatitatehadchargeularmomentum）.Youonlykyofitsdiet，notaboutthequality.Theno-hairtheorem'desChapter2saysthattheblackholeisonlycharacterizedbyaveryfewparameters（mass，dangularmomentum），aalkaboutwhattheblaadeof.
Thislaowledgeaboutthehasbeensubyablaayseemlikeatrivialobservation，butitisactuallyratherprofound.Informationaboutablackhole'slunuhasbeeallylost.Anymatterwhichhasfallenintotheblackholehassurresidentity.We'tperformmeasurementsonthatmatter，ordisydetailsaboutit.
Blackholesandengines
Thissituationiseerilyfamiliartothosewhohavestudiedthebeautifulsubjeodynamithatfielditisquiteoandhowinformatioordissipatedthroughphysicalprocesses.Thermodynamicshasalongainghistory.Themoderntheanduririalrevolutionwheryingtoworkouthowtomakesteamengi.Energy'couldbedefinedinsuchawaythatitwasalwaysservedandcouldbevertedbetweeforms.Thisisknowlawofthermodynamics.Hhyoumakesomesbetweeypesy，therearepartiversiopermittedtomake.Forexample，althoughyouareallowedtoeipletelyi（youdothateverytimeyouusethebrakestyourpletestop），youvertheatpletelyintomeicalwork，whifortunatelyispreciselyouldliketodowithasteamehereforeasteamerainonlysumakingapartialofheatfromthefuromeicalworkwhisthewheels.Itwasultimatelyrealizedthatheatisatypeyinvolvingtherandommotionofatoms，whilemeicalworkiheatedmotionofsebitofmatter，likeaiston.Therefore，apoheisrandomness:becauseofthejigglingofatomsinahotbody，youlosetraotionoftheindividualatoms.Thisrandommotionplybeuadditionalcost.Theraogiveittheteame，entropy，inaemneverdecreasesbutmustalwayseitherstaythesameorineveryphysicalprocess.（ThisistheseodynamiewayoflookingatthisistosaythatourinformationabouttheworldalwaysdecreasesbecausetraotionofalltheatomsieAsenergymovesfrommacroscopicsicroscopicsplemovingpistontotherandommotionofhugeoms，theninformationislosttous.Thermodynamicsallowsustomakethisvague-soundingnotioitative.Thisinformationlossturnsouttobeexaalogoustowhatwe'vebeendesatterfallingintoablackhole.
AlthoughthermodynamicsedforsteameheprihoughttoapplytoallprotheUhefirstpeopletothinkaboutthisihblackholeswastheOxfordphysicistRogerPenrose.Hereasobecauseablackholehasspin，itmightbepossibletyfromitandthustouseitassomekindofengine.Hecameupwithaningeniousswhichmatteristhroinningblasuchawaythatsomeeswithmythanwasthrownin.Eedfrionjustoutsidetheeventhorizon（infatheergospheredisChapter3）.Penrose'sprocessslowstherotationoftheblackhole.Inprinenormousamountybeextraablathisway，butofcoursethisisjustathoughtexperimentaseemtobeatpresentapracticalsolutioh'sloycrisis!Withinafeenrose'swork，JamesBardeen，BraephenHawkingmadealandmarkadvanulatedwhattheycalledthethreelawsofblaicswhichlaidthefoundati'slaterthinkihermodynamicsofblackholes，whichrequiredtheperatureforablackholewhichisdetermismassandspin.
Blackholesaropy
Penrose'sinsightwasasignifitimpetusandgotothersthinkingaboutthethermodynamicsofblackholes.TogetherwithR.M.Floyd，heshowedthatinhisimagiheareaoftheblackhole'seventhorizooiephenHawkingstartedwonPenrose'scleverscheme.Theareadependsonthemassandspin（andaratherplicatedway，butHawkingrovethatinanyphysicalprocessthisareaalwaysinainsthesame.Ohecesofthisintriguihatiftwoblackholescoalestheareaoftheblackholeeventhorizonedblackholesislargerthaheareasofthetwinalblackholeeventhorizons.（Thisisintuitivelyreassuriheradiusoftheeventhorizohmass，andsurfaceareahasawell-knowndependenradius.）Thisisthesamesortofbehaviourthatweseewithentropyinthermodynamidthereforepeoplebegahertheentropyofabladitsareaweresomehowected.Isthismorethanjustainganalogy?OneofJohnWheeler'sstudents，JasteiaheadandproposedadireehisPhDthesis.Bekeheideasfromtheinformatiohermodynamicstuethattheareaofablackholeeventhorizonisproportionaltoitsentropy.（Theademeansthatyoutaketheareaoftheeventhorizonanddividebyoneofphysicists'fualts，thePlanckarea，whichisroughly10-70squaremetres，andwithinanumericalfactettheentropy.Thisakestheentropyofablackholeabsolutelyenormous.）
InitiallyHawkingdidn'tbelieveBekenstein'sresults，butonfurtherexaminationhewasablenotonlytotheapproachbutdeepeandingofhowblaodynamicsworks.Itisperhapswhowtheseanalysesaredonesooneappreciateboththeirpowerbutalsotheirlimitations.Theidealwayforwardinthisfieldwouldbetouseabinationofquantummedgey，calledquantumgravity，tostudysystemswhicharebothverysmall，likeasingularityinablackhole，butinlaysabigrole.Unfortuhaveagoodtheoryofquantumgravityatpresent.Agoodapproachistousegeytomodelhowspacetimedtheogetherwithquaouhebehaviourofpartithecurvedspacetime.ThisroachthatHawkingtooktoattempttouhethermodynamicsofblackholes.
&yspaceempty?
&ofthevacuum（aregiohereisnothing'there）hashadalongandtortuoushistory.MostoftheaGreekphilosophershatedtheidea，ongroundsthattodayseemextraordinarilyare，buttherewereasmallbandofatomistswhoihevatheirdesoftheworld.Uifiaissaheideaofthevacuumwasthereforeverymuchoutoffashion.However，followiionoftheairpumpin1650，thevacuumwassomethingthatyoucouldexperimee.Eventhoughtheamountofairthatyoupoutofavesselihturystillgaveyouaratherpoorvacuumbymodernstandards，theideaofnothingnesshadbeesubstantiallymorebelievable.Oeomshadbeeedbeyondallreasoihtury，theideaiohnoatomsionlyuntroversial，butiable.
omsbeeedthaheoryofphysicsarose:quantummeiecesofthishattherewerefleetiswhenitseemslikeebeserved.Thefirstlawofthermodynamics，thegrandandseeminglyunbreakableprincipleofphysisistedthatateverymomentandateveryplacetherehadtobeastritaweesandes.Ealwaysbalahuheitant.Infact，itseemsthattheUniversalacyrulesaremoreleispossibletoobtaiisperfectlyacceptabletyforashortperiodoftimeaslongasyoupayitbackquicklyafterwards.Theamountyouborrowdepeionoftheloan，byanamountdescribedbytheHeiseyprinple，eveninthesupposedly-emptyvacuumitispossibletheomakeapartiti-particlepair.Thesetwoobjewieheremelyshortperiodaher，therebypayingtheenergybathemaximumallowedtimelimit（atimeintervalwhichisshorterthemyisborrowed）.Suchaprocessgoesohetime.Itbemeasured!Wehatthevacuumisapty，butisasoupofthesepairsofso-calledvirtualpartikinginandoutofexistehevaotsterileanduisteemingwithquantumactivity.
BlackholeevaporationandHawkingradiation
Hawkihemoderhevatumfieldtheory，tostudyitsbehaviourclosetotheeventhorizonofablackhole.Hisanalysiswasmathematicalbutictureitinquiteasimpleway.Theesseapairofvirtual'particles，apartiditsantiparticle（oppositeiimass），createdclosetotheeventhorizonofablaayeornapartfromoher.Ifopair，eithertheparticleortheanti-particle，fallsihorizonitwillpluhesingularityandeverrecovered.However，itspartsidetheblackhole.Thisparticlehaslostitsvirtualpartishelessarealpartidhasthepossibilityofescape.Iftheparticledoesescape，ratherthanfallingba，itformspartofsomethingcalledHawkingradiation.Asfarasadistantobserverised，theblackholehaslostmassbecauseaparticlehasbeehadbee，takingafieldtheory，blackholesareelyblack，buttheyactuallyemitparticles.Thisargumentalsoappliestophotons，andsoveryweaklight（alsokromagiergesfromablackholeifHawking&#umentiscorrect.
Allbodiesatemperatureemitthermalradiationasphotons.Youdothisyourself，ouldshowuponaninfra-redcameraeveninthedark（andthisiswhythepolidthemilitaryusesuchcameras）.Thehotterthebody，thehigherthefrequeioiiopokerishotevisiblelight.BecauseablaitsHawkingradiation，ithasatemperature（knownastheHawkiure）aswehaveseehoughthisisnormallyincrediblylow.AblackholewithamassofohatoftheSunhasaHawkiurelessthanabillionthofadegreeaboveabsolutezero（whichis273degreesbelpoihisisonereasonwhyHawkingradiationhased:itisincrediblyweak.Butitisbelievedtobethere.
Hawkingradiationdoeshoweverhaveaingtheevolutionofblackholes:itisultimatelyresponsibleforablackhole'sevehinkagainaboutthetarticles.Theeherealparticleesfromtheblackholehastobepositive，butsiualparticlepairappearedspontaneouslyfromthevathevirtualparticlesutotheblausthaveopensate.Beergyandmassareected，thehisprocessisthattheblackholehashadivemassaddedtoit，asmasswillhavedecreasedduetotheemissionofHawkingradiation.
Hawkinghadthereforediseismbywhichablackholeevaporate.Slowly，overtime，theblackholewillemitradiatiohisproitiallyincrediblyslow.Itturnsoutthatthelargerablackholeisthesmallerisitssurfacegravity'.Thisisbethoughthesurfacegravitydependsonmass，whichislargerfblackhole，gravitationalattrafollowsaninverse-squarelawandmoremassiveblackher.Thehatlargeblackholeshaveverylittlesurfacegravityaoaverylowtemperature.AlargeblackholethereforeemitslessHawkingradiationthanasmallblackhole.
However，asablackholeevaporatesaheamountofHawkingradiatiohesurfacegravityaureincreases.Assumingtheblackholeisn&#ahismakestherateofmasslossfasterail，attheendofitslife，theblaplypopsoutofexistehelifeofabladsnotwithabangbutop.Thisevaporationprolypossibleforblackholeswhosetemperaturesarehigherthantheirsurroundings.Atthetepoichistory，thetemperatureoftheUniverse，measuredfromthespectralshapeoftheicrowaveBadradiation，is2.7degreesaboveabsolutezero.Blackholeswithmassesgreaterthanahundredmillionmillionkiloswilleatthetepochbecausetheirtemperaturesarelowerthanthatoftheirsurroundings.TheseblackholeswhichhaveasleionofthemassoftheSun，however，willbeabletoevaporatewhentheUniversehasorefollowingfurtherexpansion.Uptothispointine，allblackholeswhosemasseswerelessthaofthisslendervalueoratedawaybynow.
Theblaationparadox
&ionwhicharisesfromallofthisiseiohematterthatfellintotheblackhole?Oneschoolofthoughtholdsthatthisinformationislostforever，eveniftheblackholesubsequees.Aofviewclaimsthatthatinformationisnotlost.Becauseblackholesevaporate，theargumeheinformatiohintheifellintotheblaustsomehowbestorediionfromtheblackhole.ThusifyoualysealltheHawkingradiationfromabladupletelyyouwouldbeabletorestructthedetailsofallthematterthathadinallyfallenintotheblackhole.Therewasafamousbetbetween，oephenHaThorne，andJohnPreskillothisverymatter.ThorneandHawkingtooktheformerposition，whilePreskilltookthelatter.Theagreementwasthattheloserihanehewinner's2004，Hawkingwassuffitlypersuadedbytheideathatinformationdeedbeeheradiationfromablackholethathecededthebet，supplyihanebaseball（whetherthatstitutesarepositoryofmeaningfulinformationdependsonyouropinionofbaseball）;however，thematterisstilldebated.
&ealltheseiheoreticalspes，itiswagainthatevenradiationfromablackholehasbeehehistoryofphysicsislitteredwiththerelicsofold，iultimatelywrong，theories.Experimentsaiolybeensurprisibringingforthus.Iioaomehatprobablyallredifirstprinciplesforblackholes.OhereasonsthatthefaintHawkingradiationhasnotbeemanyblackholesweknowaboutareattheehtestobjetheUheseblackholesarewaytoomassive，aoocold，toevaporateviaHawkingradiatiosareextrahtforapletelydifferentreason，whichisexaminedinChapter6andinChapter8.
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