Exact results in a punctured neighborhood of a strong curvature singularity

Abstract: 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 bounded on every open punctured neighborhood of the curvature singularity. Our calculations are performed using the analog 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 nontrivial constitutive relations. The regularity of the electric field as it approaches 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.