Uniqueness and energy bounds for static AdS metrics

TL;DR

This paper extends the uniqueness proof of Anti-de Sitter spacetime to certain static asymptotically hyperbolic metrics and establishes negativity of free energy for specific AdS black holes, contributing to the understanding of their geometric and thermodynamic properties.

Contribution

It adapts Wang's proof to new classes of static asymptotically hyperbolic metrics and demonstrates the negativity of free energy for higher-genus AdS black holes, advancing theoretical insights.

Findings

Uniqueness results for static asymptotically hyperbolic metrics with toroidal infinity.

Negativity of free energy for higher-genus AdS black holes.

Extension of Wang's proof to new geometric settings.

Abstract

We show that Wang's proof of uniqueness of Anti-de Sitter spacetime can be adapted to provide uniqueness results for strictly static asymptotically locally hyperbolic vacuum metrics with toroidal infinity, and to prove negativity of the free energy $E-TS$ of asymptotically AdS black holes with higher-genus horizons.