Post-Newtonian observables for aligned-spin binaries to sixth order in spin from gravitational self-force and Compton amplitudes

Accurate modeling of compact binaries is essential for gravitational-wave detection and parameter estimation, with spin being an important effect to include in waveform models. In this paper, we derive new post-Newtonian (PN) results for the conservative aligned-spin dynamics at next-to-next-to-leading order for the spina and spin4 contributions, in addition to the next-to-leading order (NLO) spin5 and spin6 contributions. One approach we follow is the Tutti Frutti method, which relates PN and gravitational self- force results through the redshift and spin-precession invariants, by making use of the simple dependence of the scattering angle on the symmetric mass ratio. However, an ambiguity arises at the NLO spin5 contribution, due to transcendental functions of the Kerr spin in the redshift; this is also the order at which Compton amplitudes calculations are affected by spurious poles. Therefore, we follow an additional approach to determine the NLO spin5 and spin6 dynamics: using on-shell Compton amplitudes obtained from black hole perturbation theory. The Compton amplitude used in this work is composed of the unambiguous tree-level far-zone part reported in [Phys. Rev. D 109, 084071 (2024)], as well as the full, noninterfering with the far-zone, l 1 / 4 2 partial wave contributions from the near zone, which are responsible for capturing Kerr finite-size effects. Other results in this paper include deriving the scattering angle of a spinning test body in a Kerr background from a parametrized worldline action and computing the redshift and spin-precession invariants for eccentric orbits without an eccentricity expansion.