Non-asymptotically flat Einstein-Scalar black hole

Abstract

Exact solutions in general relativity and other theories in physics are important. One of such theories is the Einstein-Scalar theory. We present an exact class of solutions in the Einstein-Scalar theory with a specific nonlinear self-interacting potential. The potential admits a local minimum and a local maximum in general configuration. The solutions include AdS and dS black hole and non-black hole spacetimes. The scalar field is regular on and outside the horizon and asymptotically vanishes when r -> infinity. We also study the thermal stability of the black hole solution and it is shown that the black hole is thermally stable for a certain interval of the radius of the horizon.