Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations

Abstract

We derive the radial action of a spinning probe particle in Kerr spacetime from the worldline formalism in the first-order form, focusing on linear in spin effects. We then develop a novel covariant Dirac bracket formalism to compute the impulse and the spin kick directly from the radial action, generalizing some conjectural results in the literature and providing ready-to-use expressions for amplitude calculations with generic spin orientations. This allows, for the first time, to find new covariant expressions for scattering observables in the probe limit up to $\mathcal{O}(G^6{s}_1{s}_2^4)$. Finally, we use the action-angle representation to compute the fundamental frequencies for generic bound orbits, including the intrinsic spin precession, the periastron advance and the precession of the orbital plane.

arXiv comment6 pages + appendices, 1 ancillary file; v2: typos corrected, references added

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• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
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• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• Dirac brackets for classical radiative observables
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• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
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• Unexpected Symmetries of Kerr Black Hole Scattering
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane
• Gravitational multipoles from scattering amplitudes in higher dimensions