Models of light-like charges with non-geodesic world lines

TL;DR

This paper develops models of charged massless particles moving along non-geodesic light-like paths in Minkowski space, extending classical electromagnetic fields to these less understood trajectories.

Contribution

It constructs the Maxwell field for a charged light-like particle with a non-geodesic world line, generalizing the Lienard-Wiechert field to accelerated light-like charges.

Findings

Derived the electromagnetic field near arbitrary null world lines.

Described the geometry of non-geodesic light-like trajectories.

Extended classical fields to non-geodesic light-like particles.

Abstract

Massless particles in General Relativity move with the speed of light, their trajectories in spacetime are described by null geodesics. This is independent of the electrical charge of the particle being considered, however, the charged light-like case is less well understood. Starting with the Maxwell field of a charged particle having a light-like geodesic world line in Minkowskian space-time we construct the Maxwell field of such a particle having a non-geodesic, light-like world line. The necessary geometry in the neighbourhood of an arbitrary null world line in Minkowskian space-time is described and properties of the resulting electromagnetic field are discussed. The electromagnetic field obtained represents a light-like analogue of the Lienard-Wiechert field, which generalises the Coulomb field of a charge having a time-like geodesic world line to the field of a charge having an accelerated world line.