  Advances in our understanding of perturbation theory suggest the existence of
a correspondence between classical general relativity and Yang-Mills theory. A
concrete example of this correspondence, which is known as the double copy, was
recently introduced for the case of stationary Kerr-Schild spacetimes. Building
on this foundation, we examine the simple time-dependent case of an
accelerating, radiating point source. The gravitational solution, which
generalises the Schwarzschild solution, includes a non-trivial stress-energy
tensor. This stress-energy tensor corresponds to a gauge theoretic current in
the double copy. We interpret both of these sources as representing the
radiative part of the field. Furthermore, in the simple example of
Bremsstrahlung, we determine a scattering amplitude describing the radiation,
maintaining the double copy throughout. Our results provide the strongest
evidence yet that the classical double copy is directly related to the BCJ
double copy for scattering amplitudes.
