We start from a local and linear space-time 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 space-time 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 nonabsorbing 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.

• Received 27 September 2004

DOI:https://doi.org/10.1103/PhysRevD.70.125015