Black Holes with Scalar Hair in Three Dimensions

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.