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arXiv · 2606.25792

Separability of the motion of spinning test particles in curved space-time

Vojtěch Witzany·Viktor Skoupý
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Abstract

Solving for the motion of spinning test particles in curved spacetimes is important for modeling gravitational-wave inspirals of spinning compact binaries. We build a Hamiltonian formalism in worldline-adapted tetrads for the spinning test particle and formulate a corresponding Hamilton-Jacobi equation valid to linear order in spin. We prove that when the geodesic motion in a spacetime and the parallel transport along said geodesics are both separable, then so is the corresponding Hamilton-Jacobi equation. We illustrate this in black hole, plane wave, and cosmological spacetimes.

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Vojtěch Witzany, Viktor Skoupý. 2026-06-24. Separability of the motion of spinning test particles in curved space-time. https://arxiv.org/abs/2606.25792

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