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 spin³ 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 (GSF) 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, no. 8, 084071 (2024), as well as the full, non-interfering with the far-zone, =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.