Lorentzian symmetric spaces which are Einstein-Yang-Mills with respect to invariant metric connections

Abstract

We classify four-dimensional connected simply-connected indecomposable Lorentzian symmetric spaces $M$ with connected nontrivial isotropy group furnishing solutions of the Einstein-Yang-Mills equations. Those solutions with respect to some invariant metric connection $\Lambda$ in the bundle of orthonormal frames of $M$ and some diagonal metric on the holonomy algebra corresponding to $\Lambda$.