Spontaneous Time Asymmetry due to Horizon

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1、SpontaneousTimeAsymmetryduetoHorizonRameshAnishetty,R.Parthasarathy‡TheInstituteofMathematicalSciences,Chennai-600113,INDIAWeshowthatquantizedmatterfieldsinthepresenceofbackgroundmetricswithHorizonexhibitspontaneoustimeasymmetry.Allquantizedmatterfieldshav

2、etovanishatthehorizon.Somephenemenologicalapplicationsofthisinthecontextofblackholesandearlyuniverseareconsidered.MatterinteractioninMinkowskispace-timearewellofcosmolgyafterthePlanck’stimerestsonthisassump-describedbylocalquantumfieldtheories.Thesetheori

3、estion.havePoinc´areinvariancealongwithseveralothercon-WeaddressTimereversalinvarianceofmatterfieldstinuousanddiscretesymmetries.Wedrawourattentioninthepresenceofbackgroundgravity.ThemetricistoadiscretesymmetrynamelytimereversalsymmetryMinkowskianatanyspa

4、cetimepoint;howeverglob-T.ThissaysthatthedynamicsofthematterfieldsisallyitisnotMinkowskian.Agenericbackgroundmetricsuchthatifweevolvethesystembackwardsintimeitdoesnothaveanysymmetries.Phenomenologically[7]theisperfectlyallowed,i.e.timesymmetric.Moreprecis

5、elybackgroundgravityoftheuniversedoesappeartohavethecorrelationfunctions,forinstance<φ(t)φ(t′)>assomesymmtries:howthiscomesaboutisananotherdefinedbytheFeynman’spathintegral,aresymmetricinterestingissue.Herewewillassumethattheback-functionsoft−t′[1].Whilet

6、hisisselfevidentfromgroundgravitydoeshavetimetranslationalinvariance.theLagrangianofthefundamentaltheory,thereareThatis,thereisatimelikeKillingvector.Byasuitablemanyphysicalsituationswhichdonotappeartoobeygeneralco-ordinatetransformationwecanalwayschoose

7、thissymmetry.Somewellknownexamples[2]aregiventhemetricasgivenbytheproperdistancedstobebelow.Deceleratingelectromagneticchargesradiatepho-pds2=B(~x)(A(~x)dt2−g′(~x)dxidxj),(1)tonswhilethetimereversedphenomenon,namely,theac-ijceleratingchargesabsorbingphot

8、ons,isneverallowed.′whereA,BandgijthethreedimensionalmetricareallEntropyinsufficientlylargesubspacesisalwaysincreas-timeindependent.Wefurthermadeachoiceofdefinitioningevenifthelargesubspacesarecausallydisconnected.√suchthatth