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Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame | | Luc Blanchet
; Bala Iyer
; | | Date: |
24 Sep 2002 | | Journal: | Class.Quant.Grav. 20 (2003) 755 | | Subject: | gr-qc | | 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 center-of-mass frame (center of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the center-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 center-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent, {it via} a contact transformation of the particles’ variables, to the center-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. | | Source: | arXiv, gr-qc/0209089 | | Services: | Forum | Review | PDF | Favorites | |
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