Entropy of Reissner-Nordstr\"om-like black holes

TL;DR

This paper explores the entropy and thermodynamics of Reissner-Nordström-like black holes with torsion in Poincaré gauge theory, revealing how torsion-induced parameters influence the first law of black hole thermodynamics.

Contribution

It introduces a new class of black holes with torsion, analyzing their entropy and thermodynamic properties within Poincaré gauge theory, extending previous static, spherically symmetric solutions.

Findings

The torsion parameter replaces electric charge in black hole thermodynamics.

The entropy formula remains consistent with the first law despite torsion effects.

Torsion influences the boundary term variation, ensuring thermodynamic consistency.

Abstract

In Poincar\'e gauge theory, black hole entropy is defined canonically by the variation of a boundary term $\Gamma_H$, located at horizon. For a class of static and spherically symmetric black holes in vacuum, the explicit formula reads $\delta\Gamma_H=T\delta S$, where $T$ is black hole temperature and $S$ entropy. Here, we analyze a new member of the same class, the Reissner-Nordstr\"om-like black hole with torsion [1], where the electric charge of matter is replaced by a gravitational parameter, induced by the existence of torsion. This parameter affects $\delta\Gamma_H$ in a way that ensures the validity of the first law.