Version 1
: Received: 14 September 2018 / Approved: 16 September 2018 / Online: 16 September 2018 (08:12:22 CEST)
Version 2
: Received: 5 March 2019 / Approved: 11 March 2019 / Online: 11 March 2019 (10:36:30 CET)
How to cite:
Gratus, J.; Kinsler, P.; McCall, M.W. Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge. Preprints2018, 2018090278. https://doi.org/10.20944/preprints201809.0278.v2
Gratus, J.; Kinsler, P.; McCall, M.W. Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge. Preprints 2018, 2018090278. https://doi.org/10.20944/preprints201809.0278.v2
Gratus, J.; Kinsler, P.; McCall, M.W. Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge. Preprints2018, 2018090278. https://doi.org/10.20944/preprints201809.0278.v2
APA Style
Gratus, J., Kinsler, P., & McCall, M.W. (2019). Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge. Preprints. https://doi.org/10.20944/preprints201809.0278.v2
Chicago/Turabian Style
Gratus, J., Paul Kinsler and Martin W. McCall. 2019 "Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge" Preprints. https://doi.org/10.20944/preprints201809.0278.v2
Abstract
A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
