Exact solutions of Reissner-Nordstr\"om type in Einstein-Yang-Mills --systems with arbitrary gauge groups and space-time dimensions

TL;DR

This paper introduces a broad class of exact solutions in Einstein-Yang-Mills systems with various gauge groups and dimensions, connecting symmetric solutions to lower-dimensional theories and revealing new black hole configurations.

Contribution

It develops a dimensional reduction approach to find exact Einstein-Yang-Mills solutions for arbitrary gauge groups and dimensions, including novel black hole solutions with electric and magnetic charges.

Findings

New solutions describing charged black holes in four dimensions.

An example of a nonabelian gauge solution in six dimensions.

Discussion on the stability of the solutions.

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.