Gravitational Faraday rotation of gravitational waves by a Kerr black hole

TL;DR

This paper calculates the gravitational Faraday rotation of gravitational waves lensed by a Kerr black hole, revealing tiny polarization changes that could be detectable with future GW detectors.

Contribution

It provides the first calculation of GFR angle for GWs lensed by Kerr black holes in the weak deflection limit, highlighting potential observability.

Findings

GFR causes tiny polarization rotation in lensed GWs

Rotation depends on black hole's angular momentum component

Potential detectability with third-generation GW detectors

Abstract

Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle $\chi_g$ of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle $\chi_g$ is a second-order correction to the polarization angle, which depends on the light-of-sight component of BH angular momentum. Such a rotation is tiny and degenerates with the initial polarization angle. In some critical cases, the GFR angle is close to the detection capability of the third-generation GW detector network, although the degeneracy has to be broken.