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

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arxiv 2003.07145 v1 pith:ARH3P62F submitted 2020-03-16 gr-qc astro-ph.SRhep-th

J. Blümlein , A. Maier , P. Marquard , G. Schäfer This is my paper
classification gr-qcastro-ph.SRhep-th
keywords citeberncoordinatessixthagreebinarycanonicaldamour
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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 $G_N^3$.

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