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

[摘要] We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of AdS2/CFT1correspondence. We start by shifting the horizon of near horizon extremal Kerr (NHEK) geometry by a general finite mass. While this shift does not alter the geometry in that the resulting classical solution is still diffeomorphic to the NHEK solution, it does lead to a quantum theory different from that of NHEK. We obtain this quantum theory by means of a Robinson-Wilczek two-dimensional Kaluza-Klein reduction which enables us to introduce a finite regulator on the AdS2boundary and compute the full asymptotic symmetry group of the two-dimensional quantum conformal field theory on the respective AdS2boundary. The s-wave contribution of the energy-momentum-tensor of this conformal field theory, together with the asymptotic symmetries, generate a Virasoro algebra with a calculable center, which agrees with the standard Kerr/CFT result, and a non-vanishing lowest Virasoro eigenmode. The central charge and lowest eigenmode produce the Bekenstein-Hawking entropy and Hawking temperature for NHNEK.

[发布机构] Department of Physics and Astronomy, University of Iowa, Iowa City; IA; 52242, United States^1;Department of Physics, Assumption College, Worcester; MA; 01609, United States^2;Department of Physics, Grinnell College, Grinnell; IA; 50112, United States^3;Department of Physics, Arizona State University, Tempe; AZ; 85287, United States^4

[关键词] Asymptotic symmetry;Bekenstein-Hawking entropy;Classical solutions;Conformal field theories;Diffeomorphic;Energy-momentum tensor;Microstates;Virasoro algebra