A generalized Birkhoff theorem for the Einstein–Yang–Mills system

Some results of a systematic study of the coupled Einstein–Yang–Mills (EYM) equations for arbitrary gauge groups are presented herein. In a first step a group theoretical analysis of spherically symmetric EYM fields is given. This will lead to a concise description of a large class of principal bundles for which the spherically symmetric solutions of the EYM equations have to be static (generalized Birkhoff theorem) and the metric must be of the Reissner–Nordstro/m-type.