# Gravitational rotation of polarization: Clarifying the gauge dependence and prediction for double pulsar

## TL;DR

This paper clarifies the gauge dependence of gravitational polarization rotation, emphasizing the importance of observer-lens relative motion, and predicts a measurable effect in the double pulsar system, significantly larger than previous estimates.

## Contribution

It resolves confusion in the literature regarding polarization rotation and provides an updated, larger prediction for the effect in the double pulsar system based on fundamental general relativity principles.

## Key findings

- Rotation angle estimated at ~10^{-7} rad for the double pulsar
- The effect depends explicitly on observer-lens relative motion
- Previous predictions underestimated the effect by ten orders of magnitude

## Abstract

From the basic concepts of general relativity, we investigate the rotation of the polarization angle by a moving gravitational lens. Particularly, we clarify the existing confusion in the literature by showing and explaining why such rotation must explicitly depend on the relative motion between the observer and the lens. We update the prediction of such effect on the double pulsar PSR J0737-3039 and estimate a rotation angle of $\sim 10^{-7}rad$. Despite its tiny signal, this is $10$ orders of magnitude larger than the previous prediction by Ruggiero and Tartaglia, which apparently was misguided by the confusion in the literature.