Generally covariant Fresnel equation and the emergence of the light cone structure in linear pre-metric electrodynamics

TL;DR

This paper derives a general covariant Fresnel equation for electromagnetic wave propagation in a metric-free spacetime, revealing how the light cone structure emerges from the electromagnetic constitutive relations, including effects of axion and skewon fields.

Contribution

It analytically derives the quartic Fresnel equation in pre-metric electrodynamics and shows how the light cone structure arises from the constitutive tensor's leading components.

Findings

Fresnel equation is quartic in wave covectors.

Light cone structure is induced by the principal part of the constitutive tensor.

Skewon and axion fields influence light propagation and dissipation.

Abstract

We study the {\em propagation of electromagnetic waves} in a spacetime devoid of a metric but equipped with a {\em linear} electromagnetic spacetime relation $H\sim\chi\cdot F$. Here $H$ is the electromagnetic excitation $({\cal D},{\cal H})$ and $F$ the field strength $(E,B)$, whereas $\chi$ (36 independent components) characterizes the electromagnetic permittivity/permeability of spacetime. We derive analytically the corresponding Fresnel equation and show that it is always quartic in the wave covectors. We study the `Fresnel tensor density' ${\cal G}^{ijkl}$ as (cubic) function of $\chi$ and identify the leading part of $\chi$ (20 components) as indispensable for light propagation. Upon requiring electric/magnetic reciprocity of the spacetime relation, the leading part of $\chi$ induces the {\em light cone} structure of spacetime (9 components), i.e., the spacetime metric up to a function. The possible existence of an Abelian {\em axion} field (1 component of $\chi$) and/or of a {\em skewon} field (15 components) and their effect on light propagation is discussed in some detail. The newly introduced skewon field is expected to be T-odd and related to dissipation.