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Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>6/11/2020
<mark>Journal</mark>arXiv
Publication StatusPublished
<mark>Original language</mark>English

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.