  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.
