Classical double copy: Kerr-Schild-Kundt metrics from Yang-Mills theory

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 clear-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 Gödel-type metrics along the same lines.