Black holes and the double copy

TL;DR

This paper explores the classical double copy relationship between gauge theory and gravity, showing how certain solutions like black holes and plane waves correspond across theories, extending the duality beyond perturbation theory.

Contribution

It introduces a class of gauge solutions that double copy to gravity, including Kerr-Schild metrics, and reinterprets self-dual sector relations in momentum space.

Findings

Black hole solutions double copy to gravity

Plane wave solutions are included in the framework

Self-dual sectors relate via momentum-space Kerr-Schild

Abstract

Recently, a perturbative duality between gauge and gravity theories (the double copy) has been discovered, that is believed to hold to all loop orders. In this paper, we examine the relationship between classical solutions of non-Abelian gauge theory and gravity. We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their higher-dimensional equivalents) emerge as special cases. We also discuss plane wave solutions. Furthermore, a recently examined double copy between the self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a momentum-space generalisation of the Kerr-Schild framework.