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

Understand

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.