# On the gravitational entropy of accelerating black holes

## TL;DR

This paper investigates the validity of a proposed gravitational entropy definition for accelerating black holes, analyzing various black hole types using Weyl curvature, and discusses the challenges faced in rotating charged cases.

## Contribution

It applies a phenomenological approach to evaluate gravitational entropy in accelerating black holes, extending previous methods to more complex black hole solutions.

## Key findings

- Gravitational entropy can be evaluated for different black hole types.
- The approach faces difficulties with rotating charged black holes.
- Discussion on potential reasons for the failure in certain cases.

## Abstract

In this paper we have examined the validity of a proposed definition of gravitational entropy in the context of accelerating black hole solutions of the Einstein field equations, which represent the realistic black hole solutions. We have adopted a phenomenological approach proposed in Rudjord et al [20] and expanded by Romero et al [21], in which the Weyl curvature hypothesis is tested against the expressions for the gravitational entropy. Considering the $C$-metric for the accelerating black holes, we have evaluated the gravitational entropy and the corresponding entropy density for four different types of black holes, namely, non-rotating black hole, non-rotating charged black hole, rotating black hole and rotating charged black hole. We end up by discussing the merits of such an analysis and the possible reason of failure in the particular case of rotating charged black hole and comment on the possible resolution of the problem.