Propagation features of Lorentz-violating electrodynamics

This paper explores some propagation features of electrodynamics in a Lorentz-violating scenario, focusing on a specific CPT-even term within the photon sector of the Standard Model Extension (SME). The study derives a covariant dispersion relation for light propagation in the presence of a Lorentz-violating symmetric tensor field $C_{ab}(x)$, which reveals a modified light cone structure described by a quartic polynomial. The analysis includes a simplified model where the tensor field assumes a dyadic form, leading to an effective metric that dictates the propagation. The paper investigates three distinct cases: Lorentz-violating vectors which are timelike, lightlike and spacelike, and examines their implications for the effective velocity of light, birefringence, and analogies with electrodynamics in material media. The results highlight anisotropic propagation effects and provide insights into the interplay between Lorentz violation and modified causal structures. The study concludes with a discussion of the phenomenological implications and possible experimental tests for such Lorentz-violating effects.