General relativistic dynamics of compact binary systems

Luc Blanchet

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

Comptes Rendus. Physique, Volume 8 (2007) no. 1, pp. 57-68.

Résumé
Abstract

Les équations du mouvement d'un système binaire d'objets compacts ont étées calculées dans l'approximation post-newtonienne (PN) de la relativité générale. Le niveau d'approximation atteint l'ordre 3.5PN. La partie conservative des équations du mouvement (obtenue en négligeant les termes de freinage de rayonnement) se déduit d'un lagrangien généralisé en coordonnées harmoniques, et, de façon équivalente, d'un 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 l'ordre 3PN. Nous trouvons qu'il n'y a pas de dernière orbite stable circulaire ou ISCO à l'ordre 3PN pour des masses égales.

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.

Publié le : 2007-01-01

DOI : 10.1016/j.crhy.2006.11.004

Keywords: Post-Newtonian theory, Equations of motion, Compact binary systems
Mot clés : Théorie post-newtonienne, Équations du mouvement, Systèmes binaires compacts

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     title = {General relativistic dynamics of compact binary systems},
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     pages = {57--68},
     publisher = {Elsevier},
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     number = {1},
     year = {2007},
     doi = {10.1016/j.crhy.2006.11.004},
     language = {en},
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Luc Blanchet. General relativistic dynamics of compact binary systems. Comptes Rendus. Physique, Volume 8 (2007) no. 1, pp. 57-68. doi : 10.1016/j.crhy.2006.11.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.11.004/

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