Third post-Newtonian dynamics of compact binaries: equations of motion in the centre-of-mass frame

2002/09/30 by Luc Blanchet, B. R. Iyer, Bala Iyer · 5 citations
Physics and Astronomy · #Angular momentum #Binary number #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Curvature #Equations of motion #Frame (networking) #General relativity #Geometry #Hamiltonian (control theory) #Harmonic coordinates #Lagrangian #Lagrangian and Eulerian specification of the flow field #Mathematical physics #Physics #Pulsars and Gravitational Waves Research #Quantum, superfluid, helium dynamics #Reference frame #gr-qc

paper · pdf · doi:10.1088/0264-9381/20/4/309

published as Class.Quant.Grav. 20 (2003) 755 · 31 pages, to appear in Classical and Quantum Gravity

arxiv created 2003/01/14 · openalex publication_date 2003/02/04 · openalex created_date 2016/06/24 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/06

Abstract

The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work, we investigate the binary's relative dynamics in the centre-of-mass frame (centre of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the centre-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved centre-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates centre-of-mass Lagrangian is equivalent, via a contact transformation of the particles' variables, to the centre-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.

Citations

• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Dimensional regularization of the gravitational interaction of point masses
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Effective one-body approach to general relativistic two-body dynamics
• Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Cited by

• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• Gravitational wave astronomy of single sources with a pulsar timing array
• Analytic approximations in GR and gravitational waves
• Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio
• Gravitational-wave tail effects to quartic non-linear order