Light propagation in generally covariant electrodynamics and the Fresnel equation

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Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation H=(D, 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 κ ∂ H/∂ F, at a Fresnel equation which is algebraic of 4th order in the wave covector. We determine how the different pieces of κ, in particular the axion and the skewon pieces, affect the propagation of light.