A class of rotating hairy black holes in arbitrary dimensions

TL;DR

This paper introduces a new class of exact rotating black hole solutions in arbitrary dimensions, featuring a scalar field that saturates the Breitenlohner-Freedman bound, with detailed thermodynamical and stability analyses.

Contribution

It presents novel rotating hairy black hole solutions in arbitrary dimensions with nonminimal scalar coupling and analyzes their thermodynamics and stability properties.

Findings

Mass is bounded from below by angular momentum.

Black holes are locally thermodynamically stable.

Vacuum spacetime is globally preferred over hairy black holes.

Abstract

A class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented. These spacetimes are asymptotically locally anti-de Sitter manifolds and have a Ricci-flat event horizon hiding a curvature singularity at the origin. The scalar field is real and regular everywhere and its effective mass, coming from the nonminimal coupling with the scalar curvature, saturates the Breitenlohner-Freedman bound for the corresponding spacetime dimension. The rotating black hole is obtained by applying an improper coordinate transformation to the static one. Although both spacetimes are locally equivalent, they are globally different, as it is confirmed by the nonvanishing angular momentum of the rotating black hole. It is found that the mass is bounded from below by the angular momentum in agreement with the existence of an event horizon. The thermodynamical analysis is carried out in the grand canonical ensemble. The first law is satisfied and a Smarr formula is exhibited. The thermodynamical local stability of the rotating hairy black holes is established from their Gibbs free energy. However, the global stability analysis establishes that the vacuum spacetime is always preferred over the hairy black hole. Thus, the hairy black hole is likely to decay into the vacuum one for any temperature.