The quasilocal energy and thermodynamic first law in accelerating AdS black holes

TL;DR

This paper investigates the conserved energy of accelerating AdS black holes using a novel off-shell quasilocal formalism, revealing how conical singularities influence energy and thermodynamics without extra variables.

Contribution

It introduces a new off-shell quasilocal formalism combining ADT and covariant phase space methods to analyze energy in accelerating AdS black holes.

Findings

Conical singularities significantly affect the quasilocal energy expression.

The derived energy satisfies the thermodynamic first law without additional variables.

The formalism unifies surface contributions from singularities and boundaries.

Abstract

We scrutinize the conserved energy of an accelerating AdS black hole by employing the off-shell quasilocal formalism, which amalgamates the ADT formalism with the covariant phase space approach. In the presence of conical singularities in the accelerating black hole, the energy expression is articulated through the surface term derived from our formalism. The essence of our analysis of the quasilocal energy resides in the surface contributions coming from the conical singularities as well as the conventional radial boundary. Consequently, the resultant conserved quasilocal energy naturally conforms the thermodynamic first law for the black hole without necessitating any augmentation of thermodynamic variables.