Optical Polarization Holonomy in the Kerr Metric

Abstract

Polarization holonomy is analytically determined for a class of closed, spherical trajectories of light transiting a black hole in the Kerr metric. The leading order geometric optics approximation admits a closed-form expression of such paths, and sets of source/receiver locations are quantified for a spectrum of black hole angular momenta. A conserved, conformal Yano-Killing scalar is then exploited to determine the evolving polarization. Polarization holonomy, the angle between outgoing and incoming polarizations, is quantified for the spectrum of admissible direct and retrograde trajectories. This offers a means of experimentally measuring Gravitational Faraday Rotation from a single, stationary position.