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