Solutions for gravity coupled to massless gauge fields

An explicit procedure is presented so that from each solution of the coupled Einstein-Maxwell equations for gravity and source-free electromagnetic fields, one can construct a set of solutions of the coupled Einstein-Yang-Mills equations for gravity and source-free, unquantized, massless, gauge fields for any gauge group which has an invariant metric. These solutions show that the Rainich-Misner-Wheeler "already unified field theory" cannot be extended to massless gauge fields. As an example of the procedure a solution is constructed which describes the exterior of a rotating black hole which has gauge charges such as isospin and hypercharge. A curved-space generalization of the Wu-Yang solution is shown to be a special case except written in a different gauge. Such black-hole solutions with massless gauge fields question Wheeler's "black holes have no hair" conjecture.