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

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.