Quasilocal Thermodynamics of Kerr and Kerr-anti-de Sitter Spacetimes and the AdS/CFT Correspondence

TL;DR

This paper develops a quasilocal thermodynamic framework for Kerr and Kerr-AdS black holes using minimal boundary counterterms inspired by AdS/CFT, enabling analysis across a wide parameter range beyond traditional methods.

Contribution

It introduces a novel quasilocal thermodynamics approach for rotating black holes using boundary counterterms, extending analysis capabilities beyond previous background subtraction techniques.

Findings

Computed quasilocal energy and angular momentum for various black holes.

Performed stability analysis consistent with previous infinite boundary results.

Revealed phase behavior of black holes in the quasilocal setting.

Abstract

We consider the quasilocal thermodynamics of rotating black holes in asymptotically flat and asymptotically anti de Sitter spacetimes. Using the minimal number of intrinsic boundary counterterms inspired by the AdS/CFT correspondence, we find that we are able to carry out an analysis of the thermodynamics of these black holes for virtually all possible values of the rotation parameter and cosmological constant that leave the quasilocal boundary well-defined, going well beyond what is possible with background subtraction methods. Specifically, we compute the quasilocal energy $E$ and angular momentum $J$ for arbitrary values of the rotation, mass and cosmological constant parameters for the 3+1 dimensional Kerr, Kerr-AdS black holes and 2+1 dimensional BTZ black hole. We perform a quasilocal stability analysis and find phase behavior that is commensurate with previous analyses carried out at infinity.