Abstract
We consider the equations of covariantly constant vector fields (CCVF) in a space with torsion determined by its trace. The latter is interpreted as a form of the electromagnetic (EM) 4-potentials and, on a fixed metric background, turns out to be fully determined by the CCVF equations. When the metric is Minkowskian, the above equations possess two topologically distinct solutions, with the associated EM fields being asymptotically of Lienard-Wiechert type and having distributed sources, with a fixed (“elementary”) value of the electric charge. One of the solutions is everywhere regular whereas the other is singular on a 2-dimensional shell. The propagation speed of the EM fields depends on the local charge density and only asymptotically approaches the speed of light.
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Kassandrov, V.V., Rizcallah, J.A. Regularized Lienard-Wiechert fields in a space with torsion. Gravit. Cosmol. 21, 273–278 (2015). https://doi.org/10.1134/S0202289315040088
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DOI: https://doi.org/10.1134/S0202289315040088