Rotating hairy black hole and its microscopic entropy in three spacetime dimensions

TL;DR

This paper introduces a rotating hairy black hole in three-dimensional gravity with a scalar field, analyzing its properties, asymptotic behavior, and microscopic entropy via the Cardy formula, highlighting a new ground state solution.

Contribution

It presents a new rotating hairy black hole solution with a scalar field in three dimensions and derives its microscopic entropy using a novel ground state and symmetry considerations.

Findings

Finite mass and angular momentum of the black hole.

Existence of a scalar soliton as the ground state.

Matching microscopic entropy with semiclassical calculations.

Abstract

We present a spinning hairy black hole in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. The black hole is characterized by having a single horizon which encloses a curvature singularity and the scalar field is regular everywhere. The mass and angular momentum are shown to be finite. The presence of a scalar field with a slower fall-off at infinity leads an anti-de Sitter asymptotic behavior which differs from the one found by Brown and Henneaux, but has the same symmetry group as in pure gravity. A scalar soliton, which is a finite mass regular solution devoid of integration constants, plays the role of the ground state. The existence of this soliton is the key to derive the semiclassical entropy of the rotating hairy black hole using the counting of microscopic states provided by the Cardy formula.