A Class of Integrable Metrics and Gauge Fields

TL;DR

This paper analytically solves Einstein-Yang-Mills equations for a broad class of four-dimensional spacetimes with specific symmetries, revealing new integrable metrics and gauge field configurations.

Contribution

It introduces a new class of integrable metrics and gauge fields by solving Einstein-Yang-Mills equations under specific symmetry assumptions.

Findings

Derivation of explicit solutions for Einstein-Yang-Mills equations.

Identification of a broad class of integrable metrics and gauge fields.

Insights into symmetry inheritance in gauge fields.

Abstract

Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is assumed that the gauge field inherits the symmetries of the background and is aligned with the principal null directions of the spacetime.