General Static Spherical Solutions of d-dimensional Charged Dilaton Gravity Theories

TL;DR

This paper derives the most general static, spherically symmetric solutions in d-dimensional Einstein-Maxwell-Dilaton theories, unifying known solutions and discovering new ones without assuming asymptotic conditions.

Contribution

It provides a comprehensive method to obtain exact solutions in d-dimensional Einstein-Maxwell-Dilaton theories, including new solutions with finite radius ranges, generalizing previous results.

Findings

Includes asymptotically flat GHS solutions

Contains non-asymptotically flat CHM solutions

Finds new solutions with finite allowed radius

Abstract

We get 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, 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).