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

TL;DR

This paper classifies four-dimensional Lorentzian symmetric spaces that admit solutions to Einstein-Yang-Mills equations using invariant metric connections, focusing on spaces with specific symmetry and holonomy properties.

Contribution

It provides a classification of Lorentzian symmetric spaces that support Einstein-Yang-Mills solutions with invariant metric connections, a novel insight into geometric structures compatible with gauge theories.

Findings

Identified specific Lorentzian symmetric spaces supporting Einstein-Yang-Mills solutions.

Characterized solutions with respect to invariant metric connections and diagonal holonomy metrics.

Extended understanding of geometric conditions for Einstein-Yang-Mills compatibility.

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 $\Lambda$.