Regularized Lienard-Wiehert fields in a space with torsion

TL;DR

This paper explores a modified Weyl geometry with torsion, deriving electromagnetic fields that resemble Lienard-Wiechert potentials, including a regular solution with finite charge and a singular shell solution, revealing novel propagation properties.

Contribution

It introduces a new geometric framework with torsion that yields electromagnetic solutions with unique topological and regularity properties, expanding the understanding of covariantly-constant vector fields.

Findings

One solution is everywhere regular with finite charge.

The other solution is singular on a 2D shell.

EM field propagation speed depends on local charge density.

Abstract

A natural modification of the equations of covariantly-constant vector fields (CCVF) in Weyl geometry leads us to consider a metric compatible geometry possessing conformal curvature and torsion fully 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 set Minkowskian, the named equations possess two topologically distinct solutions, with the associated EM fields being asymptotically of the 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 - singular on a 2-dimensional shell. The speed of propagation of EM fields depends on the local charge density and only asymptotically approaches the speed of light