We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of AdS2/CF T1 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/CF T 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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We study the thermodynamics of the near horizon of near extremal Kerr geometry (near − N HEK) within an AdS2/CF T1 correspondence. We do this by shifting the horizon by a general finite mass, which does not alter the geometry and the resulting solution is still diffeomorphic to N HEK, however it allows for a Robertson Wilczek two dimensional Kaluza-Klein reduction and the introduction of a finite regulator on the AdS2 boundary. The resulting asymptotic symmetry group of the two dimensional Kaluza-Klein reduction leads to a non-vanishing quantum conformal field theory (CF T ) on the respective AdS2 boundary. The s-wave contribution of the energy-momentum-tensor of the CF T , together with the asymptotic symmetries, generate a Virasoro algebra with calculable center and non-vanishing lowest Virasoro eigen-mode. The central charge and lowest eigen-mode reproduce the near − N HEK Bekenstein-Hawking entropy via the statistical Cardy Formula and our derived central charge agrees with the standard Kerr/CF T Correspondence. We also compute the Hawking temperature of the shifted near−N HEK by analyzing quantum holomorphic fluxes of the Robinson and Wilczek two dimensional analogue fields.

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