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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/2707

Title: Third post-Newtonian dynamics of compact binaries: equations of motion in the centre-of-mass frame
Authors: Blanchet, Luc
Iyer, B.R.
Issue Date: Feb-2003
Publisher: IOP Publishing Ltd.
Citation: Classical and Quantum Gravity, 2003, Vol.20, p755-776
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.
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI: http://hdl.handle.net/2289/2707
ISSN: 0264-9381
Alternative Location: http://arxiv.org/abs/gr-qc/0209089
Copyright: 2003 IOP Publishing Ltd.
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