Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory

TL;DR

This paper explores the classical double copy correspondence for Kerr-Schild-Kundt metrics in higher dimensions, showing exact solutions relate Einstein-Yang-Mills systems to scalar equations, with complexities beyond simple pp-waves.

Contribution

It demonstrates that in the Kerr-Schild-Kundt class, solutions of scalar equations can generate exact Einstein-Yang-Mills solutions, extending the double copy idea beyond simple pp-waves.

Findings

Exact solutions for Einstein-Yang-Mills systems using scalar equations.

Double copy correspondence is more complex in general KSK metrics.

Gauge fields couple dynamically to gravity, not as test fields.

Abstract

The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in $d$-dimensions in the context of possible new examples of this idea. We first show that it is possible to solve the Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon type scalar equation when the metric is the $pp$-wave metric which is the simplest member of the KSK class. In the more general KSK class, the solutions of a scalar equation also solve the Yang-Mills, Maxwell and Einstein-Yang-Mills-Maxwell equations exactly albeit with a null fluid source. Hence in the general KSK class, the double copy correspondence is not as clean-cut as in the case of the $pp$-wave. In our treatment all the gauge fields couple to dynamical gravity, and are not treated as test fields. We also briefly study G\"{o}del type metrics along the same lines.