Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields

In the current article, the classical analog of the minimal photon sector in the Lorentz-violating Standard-Model extension (SME) is investigated. The analysis is based on describing a photon classically by a geometric ray that satisfies the eikonal equation. The action principle, which leads to the eikonal equation in conventional optics, is demonstrated to work in most (but not all) Lorentz-violating cases as well. Furthermore it is found that the integrands of the action functional correspond to Finsler structures. Based on these results, Lorentz-violating light rays in a weak gravitational background are treated through the use of the minimal-coupling principle. This allows for obtaining sensitivities on Lorentz violation in the photon sector by measurements of light bending at massive bodies such as the Sun. The computations are carried out for the currently running ESA mission GAIA and the planned NASA/ESA mission LATOR. Finally, a range of aspects of explicit Lorentz violation for photons is discussed in the Finsler setting.