  The double copy of the Coulomb solution in three dimensions is a non-vacuum
solution that can be obtained through different matter couplings. It is the
static black hole solution of Einstein-Maxwell theory or general relativity
minimally coupled to a free scalar field (with one ghost sign in the action in
both cases). We consider generalizations of these matter couplings by paying
particular attention to the regularity of the static black solution on the
gravity side and the corresponding single copy electric field in the gauge
theory. We show that i) Einstein-Born-Infeld theory yields a singular double
copy, which admits stable orbits for certain choices of parameters, with a
regular single copy electric field. ii) Black hole solutions constructed in
arXiv:2104.10172 by coupling to the scalar field exemplify mostly regular
double copies with regular single copy electric fields and also admit stable
orbits. Additionally, we use these solutions to investigate the connection
between horizons on the gravity side and electric fields on the gauge theory
side, which was previously observed in four dimensions.
