Photon propagation in Einstein and Higher Derivative Gravity

TL;DR

This paper investigates how electromagnetic waves propagate in Einstein and higher derivative gravity, revealing that curvature couplings cause subluminal photon velocities and correcting misconceptions about superluminal speeds in these theories.

Contribution

It clarifies the role of curvature couplings in photon propagation and refutes claims of superluminal velocities in higher derivative gravity theories.

Findings

Photon velocities are generally less than c in curved spacetime.

Curvature couplings cause polarization-dependent deviations from null geodesics.

Superluminal claims are due to neglecting curvature terms, which are present in Einstein gravity.

Abstract

In the wave equation obeyed by electromagnetic fields in curved spacetime 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 consequence of this is that the curvature corrections to the propagation of electromagnetic radiation 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, which exists in Einstein's gravity itself.