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.

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

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Cited by in corpus (12)

• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Radiation eikonal for post-Minkowskian observables
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• Dirac brackets for classical radiative observables
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• 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