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

J Blümlein,A Maier,P Marquard,G Schäfer

doi:10.1016/j.physletb.2020.135496

J Blümlein, A Maier + Show 2 more

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https://doi.org/10.1016/j.physletb.2020.135496

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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.

Highlights

The observation of gravitational wave signals coming from merging black holes and neutron stars [3] is a milestone in astrophysics
Ref. [2] conjectured a modified 3PM result having a softer high-energy behavior differing of the results of [1,14] in the contribution to the scattering angle χ at the level of the sixth post–Newtonian level, which can be obtained by a momentum expansion of Hamiltonians calculated to the third post–Minkowskian level, and proposed to test this by calculations ab initio
), where y and y denote the respective canonical coordinates and the differential operator D g is defined in Eq (34) of [9]. The generators of this transformation are given to the fifth post–Newtonian order by4

Summary

Introduction

The observation of gravitational wave signals coming from merging black holes and neutron stars [3] is a milestone in astrophysics. I.e. at high energies of the massive objects, the post–Minkowskian (PM) approximation [1,2,14,15,16] holds, where the third post–Minkowskian level [1,14] has been reached recently. Any of the different approaches to calculate the dynamics of two–body systems has to be constantly tested with respect to their validity in view of other approaches since the goal is the consistent derivation of predictions for observables at higher and higher post–Newtonian and post–Minkowskian levels. [2] conjectured a modified 3PM result having a softer high-energy behavior differing of the results of [1,14] in the contribution to the scattering angle χ at the level of the sixth post–Newtonian level, which can be obtained by a momentum expansion of Hamiltonians calculated third post–Minkowskian

Details of the calculation

Conclusions