Canonical connections on Riemannian symmetric spaces and solutions to the Einstein–Yang–Mills equations

Abstract

It is shown that for any principal bundle over a Riemannian symmetric space G/G0 which admits G as automorphism group, the canonical G-invariant connection satisfies the source free gauge field equations. Extending this to product manifolds V×G/G0 and assuming the metric and gauge fields decompose in a natural way, this result is still valid and the Einstein equations with gauge fields as source may also be satisfied. For G/G0, this is so automatically, but with a cosmological term present. For dimV=1 or 2, solutions are found, yielding metrics of the Robertson–Walker and Reissner–Nordstrom type.