lecture24 hawking effect for interacting field theories and bh thermodynamics

《lecture24 hawking effect for interacting field theories and bh thermodynamics》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MITOpenCourseWarehttp://ocw.mit.edu8.821StringTheoryFall2008ForinformationaboutcitingthesematerialsorourTermsofUse,visit:http://ocw.mit.edu/terms.8.821F2008Lecture24BlackholeThermodynamics(Con’d)Lecturer:McGreevyDecember2,20081ClassicalBlackholeThermodynamics(Con’d)Previouslywehavesta

2、tedthethirdlawforblackholethermodynamics.Torephrasetheresult:3rdLawofblackholethermodynamics.Extremalblackholesareunnatural.Inspiteofthis,extremalblackholesarebelovedbystringtheorists,becausethecomputationsareeasier.Inparticular,Sextr.BH(T=0)=ln(#ofgroundstates),andSUSYimpliesthatthis

3、isindependentofcouplingsandhencecanbecomputedintheweakcouplinglimit.Previouslywehavealsostatedthesecondlaw,butinwhichweonlyconsideredblackholesalone.Wenowconsideramoregeneralversionthesecondlawinwhichbothblackholesandnormalstuffareincluded:Generalized2rdLaw(GSL)ofblackholethermodynamic

4、s.[BekensteinPRD93292(1974)]AStotal=Snormalstuff+ζ~GNδStotal≥0forphysicalprocesses.whereζisanumberyettobedetermined.TheideabehindtheGSListhatitwillbepossibletobuildperpetualmachinesifitisfalse.However,thereisaproblemwiththe“lowering-the-box”energyextractionschemedescribedinapreviouslec

5、ture.Tobemorespecific,supposeweloweran(infinitesimal)boxofentropyfrom∞totheeventhorizonandextractenergyalongthewayasdescribedinthepreviouslecture.Whentheboxisattheeventhorizon,weknowthatEbox(r=rs)=0,andifweletgoatthatpoint,ΔA=0fortheblackholeaccordingtothefirstlaw.HencetheGSLisviolated.T

6、heotherlawsofclassicalblackholethermodynamicsalsocontain“flaws”:1•Flaw#1.Classicallyablackholecannotradiate,soTBH=0?•Flaw#3.Classically,theareaofeachindividualblackholemustbenon-decreasing.ButthermodynamicsshouldrequireonlythatδStotal≥0.Thustheblackholethermodynamicsandordinarythermody

7、namicsarenotingoodparallel.1TheapparentcontradictionsintheblackholethermodynamiclawscanberesolvedbyrealizingthattheblackholeentropySSek=A/~GNcontainsafactorof~,henceSBek→∞intheclassicallimit(~→0)whenAandGNarefixed.Inparticular,forthebox-loweringscenario,eventhoughthechangeinareaδAisinfi

8、nites