Light propagation in generally covariant electrodynamics and the Fresnel equation

TL;DR

This paper investigates how electromagnetic waves propagate in generally covariant electrodynamics, deriving a Fresnel equation that accounts for various spacetime relations and constitutive tensor components, including axion and skewon effects.

Contribution

It derives a 4th-order Fresnel equation for wave propagation in pre-metric electrodynamics, explicitly analyzing the influence of constitutive tensor components like axion and skewon.

Findings

Fresnel equation is algebraic of 4th order in wave covector.

Different parts of the constitutive tensor affect light propagation.

The axion and skewon pieces modify the wave behavior.

Abstract

Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation $H=({\cal D},{\cal H})$ and the field strength $F=(E,B)$. We study the propagation of electromagnetic waves in such a spacetime by Hadamard's method and arrive, with the constitutive tensor density $\kappa\sim\partial H/\partial F$, at a Fresnel equation which is algebraic of 4th order in the wave covector. We determine how the different pieces of $\kappa$, in particular the axion and the skewon pieces, affect the propagation of light.