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

TL;DR

This paper presents a new methodology combining multiple theoretical formalisms to derive the fifth post-Newtonian dynamics of binary systems, confirming recent results and providing a framework for future higher-order calculations.

Contribution

A novel approach integrating various formalisms to derive high-order binary dynamics, including the fifth post-Newtonian level, with independent confirmation of recent results.

Findings

First independent confirmation of 5PN dynamics result.

Method can be extended to higher perturbation orders.

Provides checks for future 4PM calculations.

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.