Electrodynamics of a Worldsheet of Lightlike Current

Abstract

An equation of motion is derived for a topologically cylindrical worldsheet of lightlike electromagnetic current, embedded in 3+1 dimensions in a smooth external electromagnetic field. Then it is shown that the static circle of uniformly distributed lightlike current solves this equation with the external field replaced by the self-field. From a characterisation of the singular behavior of the field strength near a general worldsheet, it is argued that the worldsheet of lightlike current has a well-defined dynamics. The energy-momentum tensor of the system and the possible coupling of the system (and its electromagnetically neutral analog) to gravitation are considered.