  By constructing a model of spacetime having a strong curvature singularity in
which causal geodesics are complete, but more generic causal curves are not, we
explicitly show that some electrostatic field configurations on that background
are regular everywhere, including \emph{there} where the spacetime ceases to be
described by a pseudo-Riemannian manifold. Our calculations are performed using
the analogue-gravity description provided by Plebanski and Tamm, according to
which the characterization of the electromagnetic field on a generic curved
background is equivalent to solving Maxwell's equations in flat space with a
matter content verifying certain non-trivial constitutive relations. The
regularity of the electric field in what could be considered the worst
conceivable physical condition, opens the door to further investigation into
the possibility of propagating signals capable of crossing a spacetime
singularity.
