Temporary Singularities and Axions: an analytic solution that challenges charge conservation

TL;DR

This paper presents an analytic solution to Maxwell's equations with a temporary singularity and axion field that challenges the traditional notion of charge conservation, illustrating how physical laws constrain phenomena even at singularities.

Contribution

It introduces a novel analytic solution demonstrating charge non-conservation in a spacetime with a temporary singularity and axion field, expanding the understanding of electromagnetic behavior in such conditions.

Findings

Constructed an explicit solution violating charge conservation.

Showed the solution's applicability through transformation optics.

Highlighted constraints imposed by physical laws at singularities.

Abstract

We construct an analytic solution to Maxwell's equations that violates global charge conservation, by building on the possibilities demonstrated in [Foundations of Physics 49, 330 (2019)]. The construction is valid for a spacetime containing a temporary singularity and a Maxwellian electrodynamics containing a proposed "topological" axion field. As such, it demonstrates that although "physics breaks down" at a singularity, the physical laws on the spacetime still impose constraints on what can happen. Further, the concepts of transformation optics can be applied to show that our specific mathematical solution has a much wider applicability.