Scalar hairs and exact vortex solutions in 3D AdS gravity

TL;DR

This paper derives exact solutions for 3D AdS black holes with scalar hairs, revealing how scalar charges determine black hole mass and showing vortex solutions interpolate between different AdS vacua.

Contribution

It provides new exact solutions for 3D AdS black holes with scalar hairs and vortex configurations, expanding understanding of scalar field effects in AdS gravity.

Findings

Black hole mass is algebraically related to scalar charges.

Exact vortex solutions interpolate between distinct AdS vacua.

Solutions are derived for scalar fields saturating the BF bound and with zero asymptotic mass.

Abstract

We investigate three-dimensional (3D) Anti-de Sitter (AdS) gravity coupled to a complex scalar field \phi with self-interaction potential V(|\phi|). We show that the mass of static, rotationally symmetric, AdS black hole with scalar hairs is determined algebraically by the scalar charges. We recast the field equations as a linear system of first order differential equations. Exact solutions, describing 3D AdS black holes with real spherical scalar hairs and vortex-black hole solutions are derived in closed form for the case of a scalar field saturating the Breitenlohner-Freedman (BF) bound and for a scalar field with asymptotic zero mass. The physical properties of these solutions are discussed. In particular, we show that the vortex solution interpolates between two different AdS_{3} vacua, corresponding respectively to a U(1)-symmetry-preserving maximum and to a symmetry-breaking minimum of the potential V.