霍金与黑洞学说【英文】Hawking

Outline:ThescientistInformationandblackholesHawkingradiationDetectionofblackholesBetsonblackholes3June2006HawkingandBlackHolesTheScientistBorn19421stclasshonoursfromOxford,after“notverymuchwork”SymptomsofALSduringOxfordyearsPhDandResearchFellowinCambridgeDiscoveredHawkingradiationin1974“ABriefHistoryofTime”publishedin1987NumeroushonorarydegreesandawardsOutspokenforworldpeace,welfareofthehandicapped,andothercurrentissuesAmyotrophicLateralSclerosis肌萎縮性脊髓側索硬化症AlsocalledLouGehrig’sdiseaseSymptoms:Difficultystanding,walking,orrunningClumsiness–FrequenttrippingorfallsDifficultywithfinehandmotionssuchasbuttoning,writing,turningakeyinalockAtrophyofhandmusclesAtrophyoftongueDifficultychewingfoodDifficultyswallowing(dysphagia)DifficultyspeakingMusclecramp4BlackHoleBlackholesrepresentthefinalvictoryofgravity.Ablackholeisblackbecausegravityissostrongthatlightcannotescape.TheescapevelocityatadistancerfromthecenterofanobjectwithmassMisTheescapevelocityincreaseswithmassanddecreaseswithradius.Ifvescape>c,thenlightcannotescapeandwehaveablackhole.Lightrays5SpaceWarpsIfweimaginethespacetimeasa“rubbersheet”,thenanymasswouldproducewarpingsinit.Sinceblackholesproduceverystronggravity,spacetimeissignificantlywarped(curved)aroundthem.Weseestronglight-bendingandgravitationalredshift.6TheBlackHoleRadiusForanymass,thereisasmallestradiusbeyondwhichtheobjectbecomesablackhole.ThissmallestradiusrsiscalledtheSchwarzschildradius.Hawking:Thisdefinesthesizeofablackhole,anditdependsonthemassonly.AnythingsmallerthanitscorrespondingSchwarzschildradiusbecomesablackhole.7DissectingaBlackHoleAnon-rotatingblackholeisparticularlysimple.Thereisapointatthecentercalledthesingularity(奇點).Ithaszerosizeandinfinitedensity.Infact,itspropertiescannotbedescribedbycurrentlyknownphysics.Theeventhorizon(穹界)isaspherecenteredatthesingularitywithradiusequaltotheSchwarzschildradiusoftheblackhole.Whatisinsidetheeventhorizoncannotbeknownbyanyoneoutsidebecauseevenlightcannotescapeout.eventhorizonsingularity8

EventHorizonandSingularity9No-hairTheoremHairheremeanssomethingcomplicated(e.g.differentstyles,colors,perms,etc…).Blackholeshavenohairbecausetheyaresimple.Onlythreethingscompletelycharacterizeablackhole(Hawking1972):massangularmomentumelectriccharge10Undergeneralphysicalconditions,thesingularityisenclosedbytheeventhorizon.Informationwithintheeventhorizoncannotbetransmittedtotheexternalworld.Wesaythesingularityisconcealedordressed.Thosewhicharenotdressedarecallednakedsingularities.Mathematically,nakedsingularitiescanexist,butphysicalconsiderationssuggestcosmiccensorship:allsingularitiesareenclosed(RogerPenrose).Hawkingbetoncosmiccensorship(andconcededtooearlyin1997).CosmicCensorshipConjecture:NatureForbidsNakedSingularity11OnewaytrafficinNature?

1.Thedisintegrationoftheeggwillneverhappeninthereversedirection(re-integration).

2.Airmoleculesdiffusingoutofthebottlewillneverprogressinthereversedirection(infusion).TimeArrow12Thereisaveryimportantlawinphysics,whichgovernsthedirectionofanyprocessinaphysicalsystem.Thisiscalledthesecondlawofthermodynamics:Theentropyofanisolatedsystemneverdecrease.ExamplethereverseisnotallowedbecomesSmallerentropyLargerentropySecondLawofThermodynamics13Ifwethrowcomplicatedobjects(withlowentropy)intoablackhole,wherehastheentropygone?

Wherehastheinformationescapedfromtheblackhole?TheInformationParadox14FourLawsofBlackHoleThermodynamicsBardeen,CarterandHawking(1973)formulatedthefourlawsofblackholephysics,analogoustothefourlawsofthermodynamics.SecondLaw Thetotalsurfaceareaofblackholesisalwaysthesameorgreaterthanbefore.Whenwethrowmatterintoablackhole,orallowtwoblackholestomerge,thetotalareaoftheeventhorizonswillneverdecrease.15timespaceAreaTheoremThisimpliesthatthesurfaceareaofablackholeisameasureoftheentropy.Ifanobjecthasnonzeroentropy,thenithasatemperature,anditmustradiate!Atfirst,Hawkinghimselfcouldnotacceptthisimplication.1617GeneralRelativityand

QuantumMechanicsGeneralrelativityandquantummechanicsaretwomajorachievementsof20thcenturyphysics.Generalrelativitydealswiththeverylarge.Quantummechanicsdealswiththeverysmall.Physicistsattemptedtounifythetwo.18HawkingRadiation(1974)WhenHawkingconsideredquantummechanics,manyofhisideasofblackholesneedtobechanged.Blackholesmayactuallyradiate!Nearthehorizon,particle-anti-particlepairscanbecreatedsothatoneescapesandtheotherfallsin.Radiationenergyfollowstheblackbodydistribution.19Inclassicalphysics,vacuummeansnothingexists.However,inquantummechanics,vacuumisactuallyaseaofvirtualparticles.Inquantummechanics,thereisaconceptcalledvacuumfluctuations.Althoughtheaverageenergyofspaceiszero,localfluctuationsofenergyareallowedbytheHeisenberguncertaintyprinciple.Energyfluctuationscreatepairsofparticlesandantiparticles(e.g.2photons).Apaircanexistmomentarilyandisthereforevirtual.Theyannihilatequickly.However,thevirtualparticlescanbecomereal,iftheintensecurvatureofthespacetimeoftheblackholeputsenergytothepair.VirtualParticles20Nearablackhole,thetidalforceissostrongthatthevirtualpairsarepulledapart.Thetwovirtualparticlescanbecome

real.RealPairsCreated21Sincethephotonscanbeformedoutsidetheeventhorizon,theycanbeemittedawayfromtheblackhole.ThisiscalledHawkingradiation.TheHawkingradiationhasablackbodyspectrum,withthetemperaturegivenbyThetemperatureiscalledtheHawkingtemperature.Itdecreaseswiththemassoftheblackhole.HawkingTemperature22Einstein(onquantummechanics):Goddoesnotplaydicewiththeuniverse.Bohr(defendingquantummechanics):EinsteinshouldnottellGodwhattodo!Hawking(onradiationfromblackholes):Godnotonlyplaysdicebutalsosometimesthrowsthemwheretheycannotbeseen.Humour:HawkingStyle23Theenergyneededtocreatetherealparticlescomesfromthegravitationalfieldoftheblackhole.Hence,theemissionofHawkingradiationreducesthemassoftheblackhole.Astheprocesscontinues,theblackholewillfinallydisappear.Thisiscalledblackholeevaporation.Smallblackholeshavealargetidalforceneartheeventhorizon,andthecreationoftherealparticlesiseasier.Hawkingradiationwillbemoresignificant.Infact,thetimerequiredforevaporationisgivenbyEvaporationofBlackHoles24BlackholewithmassaboutTimeforevaporationAman10-12secondsAbuilding4secondsTheEarth1049yearsTheSun1066yearsAgalaxy1099yearsForreference,theageoftheuniverseisabout1010years.TypicalTimeofEvaporation25Formostblackholes,theHawkingradiationistoosmalltobedetected.AblackholewithdetectableHawkingradiationmustbeverysmall,withSchwarzschildradiuscomparabletoatomicnucleus.Thereisnorealobservationalevidenceforthiskindofblackholessofar.Thesetinyblackholesarecalledprimordialblackholes,whichisbelievedtobeformedintheveryearlyuniverse.TheemissionofHawkingradiationreducestheentropyofablackhole.However,thesecondlawofthermodynamicsisnotviolated,sincewehavetocounttheentropyoftheradiationaswell.LuminosityofRadiation26Hawkingradiationsuggeststhatblackholesmusthaveafinitetemperature.ThetemperatureofablackholeisgivenbyThesmallerablackhole,thehigherthetemperature,andthereforethestrongertheHawkingradiation.Fortheprimordialblackholes,thetemperatureisextremelyhigh.SizeDependence27Iflightcannotescapeablackhole,howcanweeverfindthem?Improvementsinobservationalastronomyrenderthedetectionofblackholesmorethanatheoreticalspeculation.Nowadays,wehavefoundmanycandidatesofblackholes.ManyofthemareX-raybinaries.DetectionofBlackHoles28天鵝座X-1(雙星系統中的黑洞)29天鵝座X-1的發現源頭範圍(早期)源頭範圍(修正)七十年代發現72年春，發現HDE226868射電源與X射線源亮度相關30確定天鵝座X-1是雙星系統多普勒效應顯示，雙星系統周期為5.6日HDE226868的亮度變化顯示，星體因X-1潮汐力變長31高密度星體?X射線可在極短時間內出現變化，顯示X-1并非中子星亮度變化受光速限制，顯示X-1很小32高密度星體?引用開普勒定律，顯示X-1質量超過7個太陽質量中子星質量最高不超過4-5個太陽質量X-1不可能是中子星時至今日，已有95%把握確定X-1是黑洞33天鵝座

X-1

第一個被發現的黑洞，約有9個太陽質量，所以定是黑洞。34世紀大賭博索恩(KipThorne)賭:天鵝座x-1是黑洞霍金(StephenHawking)賭:天鵝座X-1不是黑洞35In1980s,Thornethoughtaboutwormholes,andHawkingthoughtaboutbabyuniverses.Ifanobjectfallsintoablackhole,itcouldgotoanindependentbabyuniverse.Sciencefiction?Canonetraveltothepastoranotheruniverse?Bewareofspaghettification!Implication:therecanbeinformat