http://arxiv.org/abs/2003.07145
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 $G_N^3$.
J. Blümlein, A. Maier, P. Marquard, et. al.
Tue, 17 Mar 20
37/63
Comments: 13 pages Latex