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

TL;DR

This paper derives an exact analytical formula for gravitational Faraday rotation in Kerr spacetime using the ADM split, enabling precise predictions and comparisons with numerical results for polarized light near black holes.

Contribution

It provides a new closed-form expression for gravitational Faraday rotation in Kerr spacetime within the ADM formalism, verified against numerical simulations.

Findings

Analytical GFR formula matches numerical predictions.

Coordinates used avoid singularities at the ergosphere.

Enables experimental comparison of polarization holonomy.

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.