# Gravitational birefringence of light in Schwarzschild spacetime

## TL;DR

This paper investigates how light's polarization affects its trajectory in Schwarzschild spacetime, revealing polarization-dependent offsets and instabilities through numerical and perturbative solutions of modified equations.

## Contribution

It derives and solves the Souriau-Saturnini equations in Schwarzschild spacetime to analyze gravitational birefringence effects on light trajectories.

## Key findings

- Polarization-dependent trajectory offsets grow over time.
- An instability in the transverse spin component is observed.
- Numerical and perturbative methods confirm birefringence effects.

## Abstract

We compute the gravitational birefringence of light as it undergoes gravitational lensing. To this end we re-derive the Souriau-Saturnini equations in the Schwarzschild metric and solve them numerically and perturbatively. Our main result is an offset between the trajectories of the photons of opposite polarisations, which grows with time. We also find an intriguing instability of the spin component transverse to the momentum.