SU(n)-Einstein-Yang-Mills fields with spherical symmetry

For all possible actions of SU(2) on SU(n)-principal bundles over spacetime the corresponding reduced Einstein-Yang-Mills equations are derived. These actions are classified by sets of n integers with sum zero. Only the case where some of these integers have a difference of two leads to interesting equations that may have solutions generalizing the discrete sequence of regular solutions found by Bartnik and McKinnon (1988). For actions when no two integers differ by two the underlying spacetime metric is necessarily Reissner-Nordstrom.