Testing binary dynamics in gravity at the sixth post-Newtonian level. (English) Zbl 1473.83011
Summary: 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 [Z. Bern et al., “Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order”, Phys. Rev. Lett. 122, No. 20, Article ID 201603, 7 p. (2019; doi:10.1103/PhysRevLett.122.201603); T. Damour, “Classical and quantum scattering in post-Minkowskian gravity”, Phys. Rev. D (3) 102, No. 2, Article ID 024060, 42 p. (2020; doi:10.1103/physrevd.102.024060)]. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in [Bern et al., loc. cit.] or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to [Bern et al., loc. cit.], but not to [Damour, loc. cit.]. This implies that we also agree on all observables with [Bern et al., loc. cit.] to the sixth post-Newtonian order to \(G_N^3\).
MSC:
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 70F05 | Two-body problems |
| 70H15 | Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics |
| 81T12 | Effective quantum field theories |
| 81T18 | Feynman diagrams |
| 81U05 | \(2\)-body potential quantum scattering theory |
Software:
FORMReferences:
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