A New Class of Exact Hairy Black Hole Solutions

TL;DR

This paper introduces a new class of exact black hole solutions with scalar hair in anti-de Sitter space, exploring their stability, thermodynamics, and phase transitions, extending previous conformally invariant solutions by including a parameter that breaks conformal invariance.

Contribution

The authors present a novel family of black hole solutions with scalar hair characterized by a parameter g, generalizing the MTZ solution and analyzing their stability and phase behavior.

Findings

Solutions are perturbatively stable for negative mass.

Existence of a critical temperature with a higher-order phase transition.

Discovery of a branch of solutions with a first-order phase transition depending on g.

Abstract

We present a new class of black hole solutions with minimally coupled scalar field in the presence of a negative cosmological constant. We consider a one-parameter family of self-interaction potentials parametrized by a dimensionless parameter $g$. When $g=0$, we recover the conformally invariant solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing $g$ signals the departure from conformal invariance. All solutions are perturbatively stable for negative black hole mass and they may develop instabilities for positive mass. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on $g$ and it is higher than the MTZ critical temperature. As $g\to 0$, this second critical temperature diverges.