Photon propagation in Einstein and higher derivative gravity Original Research Article

We derive the wave equation obeyed by electromagnetic fields in curved space-time. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation-dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame is, in general, less than c. A physically relevant consequence of the analysis is that the curvature corrections to the propagation of electromagnetic radiation (in an homogenous and isotropic space-time) keep the velocities subluminal provided the strong energy condition is satisfied. We further show that the claims of superluminal velocities in higher derivative gravity theories are erroneous and arise due to the neglect of Riemann and Ricci coupling terms in the wave equation of Einstein gravity.