General-relativistic celestial mechanics. I. Method and definition of reference systems

Journal Article · Wed May 15 00:00:00 EDT 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.3273· OSTI ID:5541014

Damour, T ^[1]; Soffel, M; Xu, C ^[2]

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1. Institut des Hautes Etudes Scientifiques, 91440 Bures sur Yvette, France (FR) Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX, France (FR)
2. Theoretische Astrophysik, Universitaet Tuebingen, Auf der Morgenstelle 10, 7400 Tuebingen, Federal Republic of Germany (DE)

We present a new formalism for treating the general-relativistic celestial mechanics of systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such {ital N}-body systems ( external problem''), (ii) the local gravitational structure of each body ( internal problem''), and, (iii) the way the external and the internal problems fit together ( theory of reference systems''). This formalism uses in a complementary manner {ital N}+1 coordinate charts (or reference systems''): one global'' chart for describing the overall dynamics of the {ital N} bodies, and {ital N} local'' charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these {ital N}+1 reference systems is a systematic use of a particular exponential'' parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue.

• OSTI ID: 5541014
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 43:10; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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GENERAL RELATIVITY THEORY
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EQUATIONS OF MOTION
GRAVITATIONAL FIELDS
MECHANICS
METRICS
UNIVERSE
DIFFERENTIAL EQUATIONS
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FIELD THEORIES
PARTIAL DIFFERENTIAL EQUATIONS
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