JT gravity and near-extremal thermodynamics for Kerr black holes in $AdS_{4,5}$ for rotating perturbations

TL;DR

This paper demonstrates that near horizon 2D Jackiw-Teitelboim (JT) gravity effectively captures the near extremal thermodynamics of Kerr black holes in AdS4 and AdS5, with specific parameterizations relating higher-dimensional thermodynamics to 2D models.

Contribution

The authors generalize near horizon limits for Kerr-AdS4 and Kerr-AdS5 black holes, establishing a precise correspondence between their near extremal thermodynamics and 2D JT gravity.

Findings

JT theory reproduces thermodynamics at small near extremal temperatures.

The temperature of the 2D near horizon geometry is related to the original temperature via a specific factor involving parameters  and chemical potential .

The 2D JT model embeds non-trivially into the higher-dimensional dual theory.

Abstract

We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum $\delta J $ and excess mass $\delta M$ is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr $AdS_4$ we hold $\delta J-\mathcal{L}\,\delta M=0 $ while for Myers-Perry(MP) type Kerr black hole in $AdS_5$ we hold $\delta J_{\varphi_{1,2}}\hspace{-0.2cm}-\mathcal{L}_{\varphi_{1,2}}\,\delta M=0$. We show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture the thermodynamics of the higher dimensional black holes at small near extremal temperatures $T_H$. We show this by generalizing the near horizon limits found in literature by parameters $\mathcal{L}$ and $\mathcal{L}_{\varphi_{1,2}}$ for the two geometries. The resulting JT theory captures the near extremal thermodynamics of such geometries provided we identify the temperature $T^{(2)}_H$ of the near horizon $AdS_2$ geometry to be $T^{(2)}_H=T_H/(1-\mu\,\mathcal{L})$ for 4d Kerr and $T^{(2)}_H=T_H/(1-\mu\,(\mathcal{L}_{\varphi_1}+\mathcal{L}_{\varphi_2}))$ for 5d Kerr where $\mu$ is their chemical potential, with $\mu\,\mathcal{L}<1$ and $\mu\,(\mathcal{L}_{\varphi_1}+\mathcal{L}_{\varphi_2})<1$ respectively. We also argue that such a theory embeds itself non-trivially in the higher dimensional theory dual to the Kerr geometries.