GENERALLY COVARIANT FRESNEL EQUATION AND THE EMERGENCE OF THE LIGHT CONE STRUCTURE IN LINEAR PRE-METRIC ELECTRODYNAMICS

Abstract

We study the propagation of electromagnetic waves in a spacetime devoid of a metric but equipped with a linear electromagnetic spacetime relation H ~ χ · F. Here H is the electromagnetic excitation [Formula: see text] and F the field strength (E,B), whereas χ (having 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" [Formula: see text] as (cubic) function of χ and identify the leading part of χ (20 components) as indispensable for light propagation. Upon requiring electric-magnetic reciprocity of the spacetime relation, the leading part of χ induces the light cone structure of spacetime (9 components), i.e., the spacetime metric up to a function. The possible existence of an Abelian axion field (1 component of χ) and/or of a skewon field (15 components) and their effect on light propagation is discussed in detail. The newly introduced skewon field is expected to be T-odd and related to dissipation.