Gravitational Faraday Rotation of gravitational waves by a Kerr black hole

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