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

TL;DR

This paper develops a covariant formalism to compute scattering and bound observables for spinning particles in Kerr spacetime, including generic spin orientations, extending previous results and providing new expressions for amplitude calculations.

Contribution

It introduces a novel covariant Dirac bracket formalism and derives new covariant expressions for scattering observables with generic spins in Kerr spacetime.

Findings

New covariant expressions for scattering observables up to (G^6 s_1 s_2^4) order.

Derived fundamental frequencies for generic bound orbits, including spin precession.

Extended the theoretical framework to include arbitrary spin orientations in Kerr spacetime.

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.