# Rotation of polarization by a moving gravitational lens

## TL;DR

This paper provides a straightforward method to calculate the rotation of polarization caused by a relativistically moving gravitational lens, accounting for arbitrary deflection angles and lens velocities, using geometric optics and special relativity.

## Contribution

It introduces a simple prescription for polarization rotation due to moving gravitational lenses applicable to any deflection angle and velocity, combining gravitational lensing and relativistic effects.

## Key findings

- Polarization rotation depends on deflection angle and lens velocity.
- The method applies to arbitrary deflection angles and relativistic lens speeds.
- Exact Lorentz transformations are used to account for lens motion effects.

## Abstract

We present a simple prescription for the rotation of polarization produced by a relativistically moving gravitational lens, applicable to arbitrary deflection angle and arbitrary velocity of the lens. When geometric optics is applicable, two independent components contribute to the total rotation of polarization: (i) in the frame of the lens the polarization vector experiences minimal rotation defined by the deflection angle (as measured by a set of remote observers, or no rotation if defined in terms of parallel-propagated tetrad); (ii) the effect of the motion of the lens on the polarization can be taken into account exactly using special relativistic Lorentz transformation of polarization. The effects of the gravitational lensing are thus parametrized by the deflection angle of the null geodesics (not necessarily small) and the motion of the lens (not necessarily with velocities much smaller than that of light).