On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry

摘要

WestudythethermodynamicsofnearhorizonnearextremalKerr(NHNEK)geometrywithintheframeworkofAdS2/CFT1correspondence.WestartbyshiftingthehorizonofnearhorizonextremalKerr(NHEK)geometrybyageneralfinitemass.WhilethisshiftdoesnotalterthegeometryinthattheresultingclassicalsolutionisstilldiffeomorphictotheNHEKsolution,itdoesleadtoaquantumtheorydifferentfromthatofNHEK.WeobtainthisquantumtheorybymeansofaRobinson-Wilczektwo-dimensionalKaluza-KleinreductionwhichenablesustointroduceafiniteregulatorontheAdS2boundaryandcomputethefullasymptoticsymmetrygroupofthetwo-dimensionalquantumconformalfieldtheoryontherespectiveAdS2boundary.Thes-wavecontributionoftheenergy-momentum-tensorofthisconformalfieldtheory,togetherwiththeasymptoticsymmetries,generateaVirasoroalgebrawithacalculablecenter,whichagreeswiththestandardKerr/CFTresult,andanon-vanishinglowestVirasoroeigenmode.ThecentralchargeandlowesteigenmodeproducetheBekenstein-HawkingentropyandHawkingtemperatureforNHNEK...