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

We study the propagation of electromagnetic waves in a spacetime devoid of a metric but equipped with a linear electromagnetic spacetime relation H similar to chi . F. Here H is the electromagnetic excitation (D, R) and F the field strength (E, B), whereas chi (having 36 independent components) characterizes the electromagnetic permittivity/petmeability 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" 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 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 chi) 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.