Exact results in a punctured neighborhood of a strong curvature singularity

TL;DR

This paper constructs a spacetime model with a strong curvature singularity where certain electromagnetic fields remain bounded near the singularity, challenging assumptions about singularity behavior and signal propagation.

Contribution

It explicitly demonstrates bounded electrostatic fields near a strong curvature singularity using an analog gravity model, revealing new insights into singularity regularity.

Findings

Electrostatic fields are bounded near the singularity.

Causal geodesics are complete, but generic causal curves are not.

Potential for signals to cross spacetime singularities.

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.