General relativistic dynamics of compact binaries at the third post-Newtonian order

2000/07/31 by Luc Blanchet, Guillaume Faye · 6 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Equations of motion #Gamma-ray bursts and supernovae #General relativity #Gravitation #Gravitational wave #Hadamard transform #Harmonic coordinates #LIGO #Mathematics #Newtonian dynamics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Regularization (linguistics) #Ricci curvature #gr-qc

paper · pdf · doi:10.1103/physrevd.63.062005

published as Phys.Rev.D63:062005,2001 · 78 pages, submitted to Phys. Rev. D, with minor modifications

arxiv created 2000/11/18 · openalex publication_date 2001/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The general relativistic corrections in the equations of motion and associated energy of a binary system of pointlike masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the metric in harmonic coordinates at the 3PN approximation. The metric is parametrized by appropriate nonlinear potentials, which are evaluated in the case of two point particles using a Lorentzian version of a Hadamard regularization which has been defined in previous works. Distributional forms and distributional derivatives constructed from this regularization are employed systematically. The equations of motion of the particles are geodesiclike with respect to the regularized metric. Crucial contributions to the acceleration are associated with the nondistributivity of the Hadamard regularization and the violation of the Leibniz rule by the distributional derivative. The final equations of motion at the 3PN order are invariant under global Lorentz transformations, and admit a conserved energy (neglecting the radiation reaction force at the 2.5PN order). However, they are not fully determined, as they depend on one arbitrary constant, which probably reflects a physical incompleteness of the point-mass regularization. The results of this paper should be useful when comparing theory to the observations of gravitational waves from binary systems in future detectors VIRGO and LIGO.

Citations

• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Testing gravity to second post-Newtonian order: A field-theory approach
• Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Cited by

• Black holes, gravitational waves and fundamental physics: a roadmap
• Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits
• Third post-Newtonian dynamics of compact binaries: equations of motion in the centre-of-mass frame
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• Analytic approximations in GR and gravitational waves
• Gravitational-wave tail effects to quartic non-linear order