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

Abstract

We calculate the motion of binary mass systems in gravity up to the sixth post–Newtonian order to the GN3 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 [1,2] by Bern et al. and Damour. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in [1] or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to [1], but not to [2]. This implies that we also agree on all observables with [1] to the sixth post–Newtonian order to GN3.