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Comptes Rendus Physique
Volume 8, n° 1
pages 57-68 (janvier 2007)
Doi : 10.1016/j.crhy.2006.11.004
General relativistic dynamics of compact binary systems
Dynamique des systèmes binaires compacts en relativité générale
 

Luc Blanchet
, Institut dʼastrophysique de Paris, UMR 7095 CNRS, université Pierre & Marie Curie, 98, bis boulevard Arago, 75014 Paris, France 

Abstract

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application, we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses. To cite this article: L. Blanchet, C. R. Physique 8 (2007).

The full text of this article is available in PDF format.
Résumé

Les équations du mouvement dʼun système binaire dʼobjets compacts ont étées calculées dans lʼapproximation post-newtonienne (PN) de la relativité générale. Le niveau dʼapproximation atteint lʼordre 3.5PN. La partie conservative des équations du mouvement (obtenue en négligeant les termes de freinage de rayonnement) se déduit dʼun lagrangien généralisé en coordonnées harmoniques, et, de façon équivalente, dʼun hamiltonien ordinaire en coordonnées ADM. Comme application nous étudions le problème de la stabilité dynamique, vis-à-vis des perturbations gravitationnelles, des orbites binaires circulaires à lʼordre 3PN. Nous trouvons quʼil nʼy a pas de dernière orbite stable circulaire ou ISCO à lʼordre 3PN pour des masses égales. Pour citer cet article : L. Blanchet, C. R. Physique 8 (2007).

The full text of this article is available in PDF format.

Keywords : Post-Newtonian theory, Equations of motion, Compact binary systems

Mots-clés : Théorie post-newtonienne, Équations du mouvement, Systèmes binaires compacts




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