Testing binary dynamics in gravity at the sixth post-Newtonian level

TL;DR

The paper derives the two-body gravitational dynamics up to 6PN order with O(G_N^3) from an effective field theory framework using Feynman amplitudes in harmonic coordinates. By constructing explicit canonical transformations, it relates harmonic, isotropic, and EOB Hamiltonians and checks consistency against known results at 5PN, as well as the 3PM predictions of Bern et al. The main finding is agreement with Bern et al. at 6PN to O(G_N^3) but a nonconfirmation of Damour's proposed 6PN isotropic contribution to the scattering angle, suggesting a discrepancy in that conjecture. Overall, the work demonstrates the power and necessity of cross-method validation and canonical-transformations in achieving reliable high-precision gravitational predictions.

Abstract

We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the $G_N^3$ terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature \cite{Bern:2019nnu,Damour:2019lcq}. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in \cite{Bern:2019nnu} or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to \cite{Bern:2019nnu}, but not to \cite{Damour:2019lcq}. This implies that we also agree on all observables with \cite{Bern:2019nnu} to the sixth post--Newtonian order to $G_N^3$.