Abstract
We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin . By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the quadratic-in-spin two-body Hamiltonian. We first evaluate the scattering angle and two-body Hamiltonian at this order in , including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate and contributions at which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously obtained results through .
- Received 4 April 2022
- Revised 4 November 2022
- Accepted 23 December 2022
DOI:https://doi.org/10.1103/PhysRevLett.130.201402
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society