The classical double copy for Taub-NUT spacetime

TL;DR

The paper extends the classical double copy from simple Kerr-Schild spacetimes to the Taub-NUT metric, exploiting its double Kerr-Schild form to construct a gauge-theory dyon as the single copy, with mass mapping to electric charge and NUT charge to magnetic charge. It further shows that this mapping survives in curved backgrounds such as de Sitter space, where the zeroth copy requires a conformal coupling to curvature. The results provide perturbative, exact evidence for the double copy beyond flat space and link to higher-dimensional Kerr-Schild generalisations, suggesting a broader curved-space double-copy structure. Together the findings strengthen the bridge between gravitational and gauge-theory descriptions in classical settings.

Abstract

The double copy is a much-studied relationship between gauge theory and gravity amplitudes. Recently, this was generalised to an infinite family of classical solutions to Einstein's equations, namely stationary Kerr-Schild geometries. In this paper, we extend this to the Taub-NUT solution in gravity, which has a double Kerr-Schild form. The single copy of this solution is a dyon, whose electric and magnetic charges are related to the mass and NUT charge in the gravity theory. Finally, we find hints that the classical double copy extends to curved background geometries.