Black Holes with Scalar Hair in Three Dimensions

TL;DR

This paper constructs three-dimensional black hole solutions with scalar hair in Einstein-Klein-Gordon theory, showing how scalar fields modify black hole properties while reducing to BTZ black holes at large distances.

Contribution

It provides new static and spinning black hole solutions with scalar hair in three dimensions, analyzing their thermodynamics and energy conditions.

Findings

Scalar hair is secondary, related to black hole mass.

Solutions reduce to BTZ black holes asymptotically.

Scalar charge ratios are fixed by mass and angular momentum.

Abstract

Three - dimensional static and spinning black hole solutions of the Einstein-Klein-Gordon system are obtained for a particular scalar field configuration. At large distances, and for small scalar field, the solutions reduce to the BTZ black hole. The scalar field dresses the black hole with secondary scalar hair, since the scalar charge is related to the conserved black hole mass and is not an independent charge. A self interacting potential is included, containing a mass term that is above the Breitenlohner-Freedman bound in three dimensions. Independence of the scalar potential from the conserved black hole charges, imposes fixed mass and angular momentum to scalar charge ratios. The thermodynamic properties as well as the energy conditions of the black hole are analysed.