  The double copy relates scattering amplitudes in gauge and gravity theories.
It has also been extended to classical solutions, and a number of approaches
have been developed for doing so. One of these involves expressing fields in a
variety of (super-)gravity theories in terms of convolutions of gauge fields,
including also BRST ghost degrees of freedom that map neatly to their
corresponding counterparts in gravity. In this paper, we spell out how to use
the convolutional double copy to map gauge and gravity solutions in the
manifest Lorenz and de Donder gauges respectively. We then apply this to a
particular example, namely the point charge in pure gauge theory. As well as
clarifying how to use the convolutional approach, our results provide an
alternative point of view on a recent discussion concerning whether point
charges map to the Schwarzschild solution, or the more general two-parameter
JNW solution, which includes a dilaton field. We confirm the latter.
