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arXiv · 1810.03411

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

Metin Gurses·Bayram Tekin
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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.

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Metin Gurses, Bayram Tekin. 2018-10-08. Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory. https://doi.org/10.1103/physrevd.98.126017

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