Exact solutions of Reissner-Nordström type in Einstein-Yang-Mills --systems with arbitrary gauge groups and space-time dimensions

Abstract

We present a class of solutions in Einstein-Yang-Mills-systems with arbitrary gauge groups and space-time dimensions, which are symmetric under the action of the group of spatial rotations. Our approach is based on the dimensional reduction method for gauge and gravitational fields and relates symmetric EYM-solutions to certain solutions of two-dimensional Einstein-Yang-Mills-Higgs-dilaton theory. Application of this method to four-dimensional spherically symmetric (pseudo)riemannian space-time yields, in particular, new solutions describing both a magnetic and an electric charge in the center of a black hole. Moreover, we give an example of a solution with nonabelian gauge group in six-dimensional space-time. We also comment on the stability of the obtained solutions.