The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism

TL;DR

This work derives the $3.5$PN radiation-reaction terms for a two-body system within the ADM Hamiltonian formalism by specializing Jaranowski–Schäfer's $N$-body Hamiltonian to $N=2$, then obtaining the instantaneous gravitational-wave energy loss and the corresponding reactive equations of motion in both Hamiltonian and Euler–Lagrangian frameworks. The dissipative dynamics are shown to be compatible with the Iyer–Will generic reaction force when appropriate gauge parameters are chosen, with explicit values for the $2.5$PN and $3.5$PN coefficients. The authors also demonstrate consistency between instantaneous energy loss and the orbital-averaged flux for quasi-circular orbits, and they provide detailed, regularized expressions for the two-body dynamics applicable to general orbits. This work advances high-precision modeling of binary inspirals, informing gravitational-wave phasing and data-analysis efforts with gauge-consistent, explicitly derived $3.5$PN radiation-reaction terms.

Abstract

We specialize the radiation-reaction part of the Arnowitt-Deser-Misner (ADM) Hamiltonian for many non-spinning point-like bodies, calculated by Jaranowski and Schaefer [1], to third-and-a-half post-Newtonian approximation to general relativity, to binary systems. This Hamiltonian is used for the computation of the instantaneous gravitational energy loss of a binary to 1PN reactive order. We also derive the equations of motion, which include PN reactive terms via Hamiltonian and Euler-Lagrangian approaches. The results are consistent with the expressions for reactive acceleration provided by Iyer-Will formalism in Ref. [2] in a general class of gauges.