Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics

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 $T_H^{(2)}$ of the $Ad{S}_2$ geometry in the Jackiw-Teitelboim theory to be $T_H^{(2)}=T_H/(1-\mu \mathcal{L})$ where $T_H$ is the BTZ temperature and $\mu$ its chemical potential with $\mu \mathcal{L}<1$.

arXiv commentpublished version

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