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

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.