  The double copy relates scattering amplitudes in gauge and gravity theories,
and has also been extended to classical solutions. In this paper, we study
solutions in three spacetime dimensions, where the double copy may be expected
to be problematic due to the absence of propagating degrees of freedom for the
graviton, and the lack of a Newtonian limit. In particular, we examine the
double copy of a gauge theory point charge. This is a vacuum solution in gauge
theory, but leads to a non-vacuum solution in gravity, which we show is
consistent with previously derived constraints. Furthermore, we successfully
interpret the non-trivial stress-energy tensor on the gravity side as arising
from a dilaton profile, and the Newtonian description of a point charge emerges
as expected in the appropriate limit. Thus, our results provide a non-trivial
cross-check of the classical Kerr-Schild double copy.
