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

Abstract

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.