Black holes and the double copy

TL;DR

The paper develops a concrete classical realization of the BCJ double copy by exploiting Kerr-Schild metrics, showing that stationary Kerr-Schild spacetimes (e.g., Schwarzschild, Kerr, and higher-dimensional analogs) have Abelian Yang-Mills single copies, with the KS scalar φ playing the common propagator and a zeroth copy to biadjoint scalars. It extends the dictionary to time-dependent solutions, including plane waves and shockwaves, which preserve the double-copy structure. The work clarifies how gravity–gauge relations emerge non-perturbatively in a KS framework and outlines open questions about gauge choices, non-KS cases, and quantum corrections, offering a roadmap for future classical and quantum investigations of the double copy.

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.