Charged black hole with a scalar hair in (2+1) dimensions

TL;DR

This paper presents an exact solution for a charged black hole with scalar hair in (2+1) dimensions, revealing how scalar and electric charges influence black hole horizons and connecting to known solutions.

Contribution

It introduces a new exact Einstein-Maxwell-scalar solution in (2+1) dimensions with non-minimal scalar coupling and analyzes horizon conditions and parameter effects.

Findings

Scalar and electric charges affect black hole horizon structure.

The solution includes a natural negative cosmological constant.

Special parameter choices recover known (2+1)D solutions.

Abstract

We obtain and analyze an exact solution to Einstein-Maxwell-scalar theory in $(2+1)$ dimensions, in which the scalar field couples to gravity in a non-minimal way, and it also couples to itself with the self-interacting potential solely determined by the metric ansatz. A negative cosmological constant naturally emerges as a constant term in the scalar potential. The metric is static and circularly symmetric, and contains a curvature singularity at the origin. The conditions for the metric to contain 0, 1, 2 horizons are identified, and the effects of the scalar and electric charges on the size of the black hole radius are discussed. Under proper choices of parameters, the metric degenerates into some previously known solutions in $(2+1)$-dimensional gravity.