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

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 $(\mathcal{D},\mathcal{H})$ 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' ${\mathcal{G}}^{ijkl}$ 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.

16 pages, in Latex, style World Scientific ws-ijmpd.cls, title changed, one new section added on "axion and skewon", text updated, will appear in Int.J.Mod.Phys.D

References in corpus (2)

• Analog gravity from field theory normal modes?
• On the derivation of the spacetime metric from linear electrodynamics

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