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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.
Monteiro et al. (Mon,) studied this question.