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arXiv · 1606.03341

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

Ananda Guneratne·Leo Rodriguez·Sujeev Wickramasekara·Tuna Yildirim
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Abstract

We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of $AdS_2/CFT_1$ 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 $AdS_2$ boundary and compute the full asymptotic symmetry group of the two-dimensional quantum conformal field theory on the respective $AdS_2$ 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.

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Ananda Guneratne, Leo Rodriguez, Sujeev Wickramasekara, Tuna Yildirim. 2016-06-10. On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry. https://doi.org/10.1088/1742-6596/698/1/012010

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