Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation

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dc.creatorDamour, Thibault
dc.creatorJaranowski, Piotr
dc.creatorSchäfer, Gerhard
dc.date1999-12-21
dc.date.accessioned2026-07-07T11:46:29Z
dc.date.available2026-07-07T11:46:29Z
dc.descriptionWe extract all the invariants (i.e. all the functions which do not depend on the choice of phase-space coordinates) of the dynamics of two point-masses, at the third post-Newtonian (3PN) approximation of general relativity. We start by showing how a contact transformation can be used to reduce the 3PN higher-order Hamiltonian derived by Jaranowski and Schäfer to an ordinary Hamiltonian. The dynamical invariants for general orbits (considered in the center-of-mass frame) are then extracted by computing the radial action variable $\oint{p_r}dr$ as a function of energy and angular momentum. The important case of circular orbits is given special consideration. We discuss in detail the plausible ranges of values of the two quantities $\oms$, $\omk$ which parametrize the existence of ambiguities in the regularization of some of the divergent integrals making up the Hamiltonian. The physical applications of the invariant functions derived here (e.g. to the determination of the location of the last stable circular orbit) are left to subsequent work.
dc.descriptionREVTeX, 21 pages, submitted to Phys. Rev. D
dc.identifierhttps://arxiv.org/abs/gr-qc/9912092
dc.identifierhttp://arxiv.org/abs/gr-qc/9912092
dc.identifierPhys.Rev.D62:044024,2000
dc.identifierdoi:10.1103/PhysRevD.62.044024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/202244
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleDynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
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