An Analytical Formula for Gravitational Faraday Rotation in the ADM Split of Spacetime

Abstract

An analytical expression is derived for the rate of gravitational Faraday rotation measured by Eulerian observers. The reference frame is a Fermi-Walker triad aligned with the spatial wave vector. Attention is restricted to the ADM split of Kerr spacetime and geometric optics. Our exact, closed-form GFR formula is implemented and verified to be consistent with numerical predictions. The approach offers a new perspective on Faraday rotation, and it allows a single Eulerian observer to compare experimentally measured polarization holonomy with analytical prediction. Sliced spacetime does not suffer from a mathematical singularity at the ergosphere associated with Boyer-Lindquist coordinates in the threading decomposition. These physically intuitive coordinates can therefore be used to analytically produce and study GFR predictions for transits of light that pierce the ergosphere.