Ultrarelativistic sources in nonlinear electrodynamics

TL;DR

This paper investigates the behavior of electromagnetic fields of rapidly moving sources in nonlinear electrodynamics, revealing delta-like shock waves and analyzing specific cases like ultrarelativistic charges in Born-Infeld theory.

Contribution

It introduces a method to derive shock wave solutions for ultrarelativistic sources in various nonlinear electrodynamics theories, including Born-Infeld.

Findings

Ultrarelativistic sources produce delta-like shock waves.

The shock wave structure depends on the specific nonlinear theory.

Explicit solution for an ultrarelativistic charge in Born-Infeld theory.

Abstract

The fields of rapidly moving sources are studied within nonlinear electrodynamics by boosting the fields of sources at rest. As a consequence of the ultrarelativistic limit the delta-like electromagnetic shock waves are found. The character of the field within the shock depends on the theory of nonlinear electrodynamics considered. In particular, we obtain the field of an ultrarelativistic charge in the Born-Infeld theory.