Entropy of black holes coupled to a scalar field

TL;DR

This paper extends the Hamiltonian approach to black hole entropy by incorporating scalar matter, analyzing black holes with scalar hair in general relativity and teleparallel gravity, confirming the first law of thermodynamics.

Contribution

It introduces a unified Hamiltonian framework for black hole entropy with scalar fields in different gravity theories, demonstrating its consistency.

Findings

First law of black hole thermodynamics holds with scalar hair

Hamiltonian approach effectively analyzes asymptotic charges

Results are consistent across GR and teleparallel gravity

Abstract

The Hamiltonian approach to black hole entropy, recently proposed in the framework of Poincar\'e gauge theory, is extended by including the scalar matter. The improved approach is used to analyse asymptotic charges and entropy of a typical black hole with scalar hair in two complementary dynamical settings, in GR and in the teleparallel gravity. In both cases, the results confirm the validity of the first law.