Journal of Physics: Conference Series
We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of AdS2/CFT1 correspondence. 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 AdS2 boundary and compute the full asymptotic symmetry group of the two-dimensional quantum conformal field theory on the respective AdS2 boundary. 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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Guneratne, A.; Rodriguez, L.; Wickramasekara, S.; and Yildirim, T. (2016). On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry. Journal of Physics: Conference Series 698: 012010. https://doi.org/10.1088/1742-6596/698/1/012010