High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system

TL;DR

This paper derives high-order post-Newtonian dynamical effects in binary systems from tail-of-tail interactions, achieving precise agreement with previous self-force and scattering results, advancing the understanding of gravitational dynamics.

Contribution

It computes dynamical observables at 6.5PN and 8th PM order from tail-of-tail interactions, providing new high-order analytical results in gravitational two-body dynamics.

Findings

Agreement with previous self-force results

Consistency with recent high-PN radiated angular momentum derivation

Alignment with state-of-the-art post-Minkowskian scattering results

Abstract

Starting from the recently derived conservative tail-of-tail action [D. Bini and T. Damour, arXiv:2504.20204 [hep-th]] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the 8th post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [A. Geralico, arXiv:2507.03442 [gr-qc]]) with state-of-the-art post-Minkowskian scattering results [M.~Driesse et al., Nature \textbf{641}, no.8063, 603-607 (2025)].