Gravity-induced birefringence in spherically symmetric spacetimes

Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light propagation in a vacuum is typically modeled by rays that follow null geodesics. However, general relativity predicts that polarization-dependent deviations from these geodesics occur in an inhomogeneous gravitational field. In this article, we evaluate the corrections for the deflection and emission of light by a massive gravitating body. Additionally, we derive the scaling behavior of the physical parameters characterizing the trajectories. The calculations are performed at leading order in frequency. We use these results to assess the significance of the birefringence effect in various astrophysical observations. We find that the effect cannot be measured with current instruments but may be detectable in the near future.