Kerr-Schild double copy for Kundt spacetimes of any dimension

Abstract

We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) - these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.

26 pages, minor changes, new references added, matches version to appear in JHEP

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• New framework for classical double copies
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• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction