千米小说网

Chapter 5 Entropy and thermodynamics of black holes（第1页）

Chapter5Entropyandthermodynamicsofblackholes

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。（Thisistheseodynamiewayoflookingatthisistosaythatourinformationabouttheworldalwaysdecreasesbecausetraotionofalltheatomsiem。Asenergymovesfrommacroscopicsicroscopicsplemovingpistontotherandommotionofhugeoms，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。