Thermodynamic relation of accelerating black holes in anti-de Sitter spacetime

TL;DR

This paper explores the thermodynamic extremality relations of accelerating black holes in anti-de Sitter spacetime, demonstrating the validity of a universal relation and its connection to cosmic string tensions and the Weak Gravity Conjecture.

Contribution

It extends the universal extremality relation to accelerating black holes and clarifies the matching conditions involving cosmic string tensions.

Findings

The Goon and Penco relation holds for accelerating black holes.

Matching conditions relate perturbation parameters to cosmic string tensions.

Extremality relations exhibit behavior similar to the Weak Gravity Conjecture.

Abstract

We consider accelerating black holes in four-dimensional anti-de Sitter spacetime and investigate the extremality relations by examining perturbative corrections to both the entropy of black holes and their extremality bounds. It is shown that the so-called Goon and Penco (univeral) relation is also valid for accelerating black holes. Furthermore, it is found that an appropriate matching condition is necessary between the perturbation parameter of the relation with the perturbative correction to such black holes, and the parameter with information about the conical deficits on the north and south poles with the cosmic string tensions in order to satisfy the extremality relations. This result indicates that the extremality (univeral) relation of a class of accelerating black holes holds exhibit behavior similar to the Weak Gravity Conjecture.