Novel approach to binary dynamics: application to the fifth post-Newtonian level

TL;DR

A new methodology for deriving the conservative dynamics of gravitationally interacting binary systems by restricting the results to the third post-Minkowskian level, which gives the first independent confirmation of the recent result of Bern et al.

Abstract

We introduce a new methodology for deriving the conservative dynamics of gravitationally interacting binary systems. Our approach combines, in a novel way, several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, and effective one-body. We apply our method to the derivation of the fifth post-Newtonian dynamics. By restricting our results to the third post-Minkowskian level, we give the first independent confirmation of the recent result of Bern {\it et al.} [Phys.\ Rev.\ Lett.\ {\bf 122}, 201603 (2019)]. We also offer checks for future fourth post-Minkowskian calculations. Our technique can, in principle, be extended to higher orders of perturbation theory.

Figures (1)

• Figure 1: Schematic representation of the theoretical tools used to obtain the various contributions to the 5PN-accurate local Hamiltonian. These contributions are keyed, on the horizontal axis, by powers of $u=GM/r$ and squared momentum $p^2 \sim p_r^2 \sim p_t^2$, and, on the the vertical axis, by powers of $\nu \equiv m_1 m_2/(m_1+m_2)^2$. The bullets indicate the coefficients determined for the first time in the present work. The question marks denote the only two missing coefficients.