gr-qc/9504004
UMDGR-95-114
ThermodynamicsofSpacetime:
TheEinsteinEquationofState
5
9TedJacobson
9
1
nDepartmentofPhysics,UniversityofMaryland
uCollegePark,MD20742-4111,USA
J
jacobson@umdhep.umd.edu
6
2
vAbstract
4
0TheEinsteinequationisderivedfromtheproportionalityofentropy
0andhorizonareatogetherwiththefundamentalrelationδQ=TdS
4connectingheat,entropy,andtemperature.Thekeyideaistodemand
0thatthisrelationholdforallthelocalRindlercausalhorizonsthrough
5
9eachspacetimepoint,withδQandTinterpretedastheenergy?ux
/andUnruhtemperatureseenbyanacceleratedobserverjustinside
cthehorizon.Thisrequiresthatgravitationallensingbymatterenergy
q
-distortsthecausalstructureofspacetimeinjustsuchawaythatthe
rEinsteinequationholds.Viewedinthisway,theEinsteinequation
g
:isanequationofstate.Thisperspectivesuggeststhatitmaybeno
vmoreappropriatetocanonicallyquantizetheEinsteinequationthan
i
Xitwouldbetoquantizethewaveequationforsoundinair.
r
a
Thefourl