Thermodynamic relation on higher-dimensional black hole with arbitrary cosmological constant

TL;DR

This paper demonstrates that the Goon--Penco relation is universally valid for higher-dimensional Reissner-Nordström black holes across various dimensions and states, including near-extremal and near-Nariai conditions, regardless of the cosmological constant.

Contribution

It extends the universality of the Goon--Penco relation to higher-dimensional black holes with arbitrary cosmological constants and diverse states.

Findings

Goon--Penco relation holds in higher dimensions.

Universality across different black hole states.

Applicable with any cosmological constant.

Abstract

We investigated the Goon--Penco (GP) relation on higher-dimensional Reissner-Nordstr\"om black holes with an arbitrary cosmological constant. It was found that the GP relation retained its form in four- and higher-dimensional spacetimes. Thus, the reactions in the black holes are universal with respect to the dimensionality. Furthermore, the GP relation was found to be universal on any state of the black hole including near-extremal and near-Nariai cases. Thus, this study showed that the GP relation was prevalent for higher-dimensional Reissner-Nordstr\"om black holes with an arbitrary cosmological constant regardless of the initial state.