Shock Wave Polarizations and Optical Metrics in the Born and the Born-Infeld Electrodynamics

TL;DR

This paper investigates shock wave behavior in nonlinear electrodynamics, revealing that Born-Infeld theory shows no birefringence while Born theory does, and introduces new polarization results for Born-type models.

Contribution

It develops a series expansion method for analyzing shock waves in nonlinear electrodynamics and derives polarization and birefringence conditions, including new results for Born-type models.

Findings

Born-Infeld theory exhibits no birefringence.

Born theory shows birefringence with polarization-dependent propagation.

New polarization characteristics are derived for Born-type electrodynamics.

Abstract

We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock wave front. This brings about a corresponding expansion of the respective electromagnetic field equations which allows for deriving relations that determine the jump coefficients in the expansion series of the potential. We compute the components of a suitable gauge-normalized version of the jump coefficients given for a prescribed tetrad compatible with the shock front foliation. The solution of the first-order jump relations shows that, in contrast to linear Maxwell's electrodynamics, in general the propagation of shock waves in nonlinear theories is governed by optical metrics and polarization conditions describing the propagation of two differently polarized waves (leading to a possible appearance of birefringence). In detail, shock waves are analyzed in the Born and Born-Infeld theories verifying that the Born-Infeld model exhibits no birefringence and the Born model does. The obtained results are compared to those ones found in literature. New results for the polarization of the two different waves are derived for Born-type electrodynamics.