Classical and thermodynamical aspects of black holes with conformally coupled scalar field hair

TL;DR

This paper reviews and extends the understanding of four-dimensional spherically symmetric black holes with conformally coupled scalar fields, focusing on their existence, stability, and thermodynamics across different cosmological constant scenarios.

Contribution

It provides a comprehensive review of known solutions and introduces new results on the thermodynamics of these black holes with non-zero cosmological constant.

Findings

Existence of black hole solutions with conformally coupled scalar hair across various cosmological constants.

Analysis of stability conditions for these black hole solutions.

New thermodynamic insights for black holes with non-zero cosmological constant.

Abstract

We discuss the existence, stability and classical thermodynamics of four-dimensional, spherically symmetric black hole solutions of the Einstein equations with a conformally coupled scalar field. We review the solutions existing in the literature with zero, positive and negative cosmological constant. We also outline new results on the thermodynamics of these black holes when the cosmological constant is non-zero.