Scattering and Bound Observables for Spinning Particles in Kerr Spacetime with Generic Spin Orientations

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 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.