General static spherical solutions of \(d\)-dimensional charged dilaton gravity theories. (English) Zbl 0925.83067
Summary: 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 flat 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 space-time dimension \(d\;(d>3)\).
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