General static spherical solutions of d-dimensional charged dilaton gravity theories

Abstract

We obtain the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions for the static equations of motion, we find field redefinitions that nearly reduce these theories to the d-dimensional Einstein-Maxwell-scalar theories, and therefore enable us to get the exact solutions. We do not make any assumption about the asymptotic space-time structure. As a result, our 4-dimensional solutions contain the asymptotically flat Garfinkle-Horowitz-Strominger (GHS) solutions and the non-asymptotically hat Chan-Horne-Mann (CHM) solutions. Besides that, we find some new solutions with a finite range of allowed radius of the transversal sphere. These results generalize to an arbitrary spacetime dimension d (d > 3).