We construct an analytic solution for electromagnetic fields interacting with an axion field that violates global charge conservation.
Despite providing a specific example where “physics breaks down” at a singularity, it nevertheless demonstrates that the physical laws on the surrounding spacetime still impose constraints on what is allowed to happen. The construction is valid for a spacetime containing a temporary singularity and a Maxwellian electrodynamics containing a proposed “topological” axion field. Further, the concepts of transformation optics can be applied to show that our specific mathematical solution has a much wider applicability.