Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair

TL;DR

This paper introduces a new family of four-dimensional asymptotically AdS black hole solutions with scalar hair, demonstrating a phase transition at a critical temperature, expanding understanding of black hole thermodynamics with scalar fields.

Contribution

The paper provides explicit solutions for hairy black holes in AdS space with a self-interacting scalar field, including the scalar potential and thermodynamic phase transition analysis.

Findings

Existence of hairy black hole solutions with scalar hair

Identification of a critical temperature for phase transition

Thermodynamic stability of the new black hole configurations

Abstract

We present a new family of asymptotically AdS four-dimensional black hole solutions with scalar hair of a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential. For a certain profile of the scalar field we solve the Einstein equations and we determine the scalar potential. Thermodynamically we show that there is a critical temperature below which there is a phase transition of a black hole with hyperbolic horizon to the new hairy black hole configuration.