Abstract
In this paper, dedicated to Larry Biedenharn on the occasion of his 70th birthday, we review and present some new results for the coupled Einstein-Yang-Mills (EYM) equations. In the spirit of the Symposium, a group theoretical analysis of spherically symmetric EYM fields for arbitrary gauge groups is emphasized. As one of the applications we will give 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-Nordstrom type. In a final section we discuss the complementary set, for which interesting black hole solutions with hair are expected to exist. In particular, the static coupled EYM equations are brought into an explicit form, which decouples partially in the generic case.
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