A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity

TL;DR

This paper develops an enhanced Komar integral for calculating mass and angular momentum of asymptotically AdS black holes in Einstein gravity, extending the traditional approach with higher-order derivative terms.

Contribution

It introduces a higher-order corrected Komar potential for asymptotically AdS spacetimes, enabling accurate conserved charge calculations in Einstein gravity with a negative cosmological constant.

Findings

Derived a new potential combining Komar and higher-derivative terms.

Validated the formula by computing mass and angular momentum for various AdS black holes.

Results match established literature values.

Abstract

The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d'Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d'Alembertian. The surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, we make use of such a formula to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results coincide with the ones in the literature.