Exact black hole solution with a minimally coupled scalar field

TL;DR

This paper presents an exact four-dimensional black hole solution in gravity coupled with a scalar field, featuring a negative curvature horizon, regular scalar field outside the singularity, and interesting thermodynamic behavior including a phase transition.

Contribution

It introduces a novel exact black hole solution with a minimally coupled scalar field in asymptotically locally AdS spacetime, highlighting unique thermodynamic properties.

Findings

The scalar field remains regular outside the singularity.

Existence of a critical temperature for scalar hair formation.

Black hole undergoes a phase transition similar to ferromagnetism.

Abstract

An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfied on and outside the event horizon. The thermodynamical analysis shows the existence of a critical temperature, below which a black hole in vacuum undergoes a spontaneous dressing up with a nontrivial scalar field in a process reminiscent of ferromagnetism.