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

TL;DR

This paper derives the third-and-a-half post-Newtonian Hamiltonian for binary black-hole systems in the ADM formalism, enabling precise calculations of gravitational energy loss and reactive dynamics.

Contribution

It extends the ADM Hamiltonian framework to third-and-a-half post-Newtonian order, providing new equations of motion including reactive terms for binary systems.

Findings

Derived the 3.5PN Hamiltonian for binary systems

Calculated instantaneous gravitational energy loss at 1PN reactive order

Validated reactive acceleration expressions against Iyer-Will formalism

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.