Gravitational radiation reaction and balance equations to post-Newtonian order

1996/09/20 by Luc Blanchet, L. Blanchet · 92 citations
Mathematics · Physics and Astronomy · #Angular momentum #Atomic physics #Classical mechanics #Cosmology and Gravitation Theories #Equations of motion #Gamma-ray bursts and supernovae #Gravitation #Gravitational field #Mathematics #Mechanics #Newtonian fluid #Physics #Pulsars and Gravitational Waves Research #Quadrupole #Scalar (mathematics) #gr-qc

paper · pdf · doi:10.1103/physrevd.55.714

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 55(2), 714-732 (American Physical Society) · To appear in Phys. Rev. D

arxiv created 1996/09/20 · openalex publication_date 1997/01/15 · arxiv updated 2011/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Gravitational radiation reaction forces and balance equations are investigated to 3/2 post-Newtonian (1.5PN) order beyond the quadrupole approximation, corresponding to the 4PN order in the equations of motion of an isolated system. By matching a post-Newtonian solution for the gravitational field inside the system to a post-Minkowskian solution (obtained in a previous work) for the gravitational field exterior to the system, we determine the 1PN relativistic corrections to the ``Newtonian'' radiation reaction potential of Burke and Thorne. The 1PN reaction potential involves both scalar and vectorial components, with the scalar component depending on the mass-type quadrupole and octupole moments of the system, and the vectorial component depending in particular on the current-type quadrupole moment. In the case of binary systems, the 1PN radiation reaction potential has been shown elsewhere to yield consistent results for the 3.5PN approximation in the binary's equations of motion. Adding up the effects of tails, the radiation reaction is then written to 1.5PN order. In this paper, we establish the validity to 1.5PN order, for general systems, of the balance equations relating the losses of energy, linear momentum, and angular momentum in the system to the corresponding fluxes in the radiation field far from the system.

Citations

• Discovery of a pulsar in a binary system
• Second-post-Newtonian generation of gravitational radiation
• Multipole expansions of gravitational radiation
• Hereditary effects in gravitational radiation

Cited by

• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
• First law of binary black hole mechanics in general relativity and post-Newtonian theory
• Transition from inspiral to plunge in binary black hole coalescences