Spherically symmetric Einstein-Yang-Mills-Higgs fields for general compact gauge groups

We discuss and classify the Einstein-Yang-Mills-Higgs (EYMH) fields that are invariant under arbitrary actions of a symmetry group by automorphisms on principal bundles with arbitrary compact gauge groups that project onto the isometries of space-time. In particular, we apply this result to the systematic construction of spherically symmetric EYMH fields in this general setting. Physically reasonable boundary conditions at infinity and/or at the center have been shown to considerably restrict the possible Yang-Mills connections. Here we investigate for which representations of the gauge group Higgs fields may be spherically symmetric or may at least contribute to a spherically symmetric stress-energy tensor.