Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics

TL;DR

This paper demonstrates that Jackiw-Teitelboim gravity effectively models the near extremal thermodynamics of BTZ black holes, incorporating excess mass and angular momentum through a new parameter, and establishes a precise temperature relation.

Contribution

The work introduces a novel parameter linking near extremal BTZ geometries to JT gravity, extending the theory's applicability to more general near extremal conditions.

Findings

JT gravity captures near extremal BTZ thermodynamics with excess parameters.

New near horizon limits of BTZ geometries are derived parametrized by 9.

The temperature relation between JT and BTZ geometries is explicitly established.

Abstract

We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of BTZ with excess mass $\delta M$ and excess angular momentum $\delta J =\mathcal{L}\, \delta M$ over extremality. We find that the Jackiw-Teitelboim theory is able to capture such departures from extremality with an additional parameter $\mathcal{L}$ relating it to the near extremal BTZ configuration. We are able to show this by obtaining new simultaneous near horizon near extremal limits of the BTZ geometry parametrized by $\mathcal{L}$. The resulting Jackiw-Teitelboim theory captures the near extremal thermodynamics of such BTZ geometries provided we identify the temperature $T^{(2)}_H$ of the $AdS_2$ geometry in the Jackiw-Teitelboim theory to be $T^{(2)}_H=T_H/(1-\mu\,\mathcal{L})$ where $T_H$ is the BTZ temperature and $\mu$ its chemical potential with $\mu\,\mathcal{L}<1$.