The Kerr-Schild double copy in curved spacetime

TL;DR

This paper explores extending the classical double copy relationship between gauge and gravity theories to curved spacetimes, using Kerr-Schild metrics and non-trivial backgrounds, with potential cosmological implications.

Contribution

It demonstrates how graviton solutions in curved space can be constructed as double copies of gauge fields on non-zero backgrounds, broadening the scope of the double copy framework.

Findings

Double copies of gauge fields on non-zero backgrounds produce graviton solutions in curved spacetime.

The double copy persists beyond Kerr-Schild backgrounds, including conformally flat metrics.

Results suggest potential applications in cosmology and curved spacetime physics.

Abstract

The double copy is a much-studied relationship between scattering amplitudes in gauge and gravity theories, that has subsequently been extended to classical field solutions. In nearly all previous examples, the graviton field is defined around Minkowski space. Recently, it has been suggested that one may set up a double copy for gravitons defined around a non-trivial background. We investigate this idea from the point of view of the classical double copy. First, we use Kerr-Schild spacetimes to construct graviton solutions in curved space, as double copies of gauge fields on non-zero gauge backgrounds. Next, we find that we can reinterpret such cases in terms of a graviton on a non-Minkowski background, whose single copy is a gauge field in the same background spacetime. The latter type of double copy persists even when the background is not of Kerr-Schild form, and we provide examples involving conformally flat metrics. Our results will be useful in extending the remit of the double copy, including to possible cosmological applications.