Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity

TL;DR

This paper reviews multiple approaches to deriving the fourth post-Newtonian two-body dynamics in general relativity, confirming some results and correcting others, highlighting the complementarity and challenges of different methods.

Contribution

It provides a comprehensive review of recent 4PN dynamics derivations, confirming some results and addressing discrepancies in the literature.

Findings

First complete 4PN derivation confirmed by subsequent works

Delaunay-averaging results validated by independent studies

Corrections to recent Fokker-action claims identified and clarified

Abstract

The fourth post-Newtonian (4PN) two-body dynamics has been recently tackled by several different approaches: effective field theory, Arnowitt-Deser-Misner Hamiltonian, action-angle-Delaunay averaging, effective-one-body, gravitational self-force, first law of dynamics, and Fokker action. We review the achievements of these approaches and discuss the complementarity of their results. Our main conclusions are: (i) the results of the first complete derivation of the 4PN dynamics [T.Damour, P.Jaranowski, and G.Sch\"afer, Phys. Rev. D 89, 064058 (2014)] have been, piecewise, fully confirmed by several subsequent works; (ii) the results of the Delaunay-averaging technique [T.Damour, P.Jaranowski, and G.Sch\"afer, Phys. Rev. D 91, 084024 (2015)] have been confirmed by several independent works; and (iii) several claims in a recent Fokker-action computation [L.Bernard et al., arXiv:1512.02876v2 [gr-qc]] are incorrect, but can be corrected by the addition of a couple of ambiguity parameters linked to subtleties in the regularization of infrared and ultraviolet divergences.