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2020

Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders

Bini, Donato, Damour, Thibault, Geralico, Andrea

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Using the new methodology introduced in a recent Letter [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian (5.5PN) level.

We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics.
Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, effective one-body, and Delaunay averaging.
We determine the full functional structure of the 5PN Hamiltonian (which involves 95 non-zero numerical coefficients), except for two undetermined coefficients proportional to the cube of the symmetric mass ratio, and to the fifth and sixth power of the gravitational constant, $G$.

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