  We start from a local and linear spacetime relation between the
electromagnetic excitation and the field strength. Then we study the generally
covariant Fresnel surfaces for light rays and light waves. The metric and the
connection of spacetime are left unspecified. Accordingly, our framework is
ideally suited for a search of possible violations of the Lorentz symmetry in
the photon sector of the extended standard model. We discuss how the skewon
part of the constitutive tensor, if suitably parametrized, influences the
Fresnel surfaces and disturbs the light cones of vacuum electrodynamics.
Conditions are specified that yield the reduction of the original quartic
Fresnel surface to the double light cone structure (birefringence) and to the
single light cone. Qualitatively, the effects of the real skewon field can be
compared to those in absorbing material media. In contrast, the imaginary
skewon field can be interpreted in terms of non-absorbing media with natural
optical activity and Faraday effects. The astrophysical data on gamma-ray
bursts are used for deriving an upper limit for the magnitude of the skewon
field.
