General Black Hole Solutions in (2+1)-dimensions with a Scalar Field Non-Minimally Coupled to Gravity

Abstract

We discuss black hole solutions in (2+1)-dimensions with a scalar field non-minimally coupled to Einstein's gravity in the presence of a cosmological constant and a self-interacting scalar potential. Without specifying the form of the potential, we find a general solution of the field equations, which includes all the known asymptotically anti-de Sitter (AdS) black hole solutions in (2+1)-dimensions as special cases once values of the coupling constants are chosen appropriately. In addition, we obtain numerically new black hole solutions and for some specific choices of the coupling constants we derive new exact AdS black hole solutions. We also discuss the possibility of obtaining asymptotically de Sitter black hole solutions with or without an electromagnetic field.