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arXiv · 2511.15639

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

Mark T. Lusk
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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.

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Mark T. Lusk. 2026-03-20. An Analytical Formula for Gravitational Faraday Rotation in the ADM Split of Spacetime. https://doi.org/10.1140/epjc%2Fs10052-026-15352-5

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