Journal ArticleDOI
General-relativistic celestial mechanics. I. Method and definition of reference systems.
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A new formalism for treating the general-relativistic celestial mechanics of systems of system of arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies is presented, aimed at yielding a complete description of the global dynamics of such $N-body systems.Abstract:
We present a new formalism for treating the general-relativistic celestial mechanics of systems of $N$ 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 $N$-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 $N+1$ coordinate charts (or "reference systems"): one "global" chart for describing the overall dynamics of the $N$ bodies, and $N$ "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 $N+1$ 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. Our scheme differs from previous attempts in several other respects: the structure of the stress-energy tensor is left completely open; the spatial coordinate grid (in each system) is fixed by algebraic conditions while a convenient "gauge" flexibility is left open in the time coordinate [at the order $\ensuremath{\delta}t=O({c}^{\ensuremath{-}4})$]; the gravitational field locally generated by each body is skeletonized by particular relativistic multipole moments recently introduced by Blanchet and Damour, while the external gravitational field experienced by each body is expanded in terms of a particular new set of relativistic tidal moments. In this first paper we lay the foundations of our formalism, with special emphasis on the definition and properties of the $N$ local reference systems, and on the general structure and transformation properties of the gravitational field. As an illustration of our approach we treat in detail the simple case where each body can, in some approximation, be considered as generating a spherically symmetric gravitational field. This "monopole truncation" leads us to a new (and, in our opinion, improved) derivation of the Lorentz-Droste-Einstein-Infeld-Hoffmann equations of motion. The detailed treatment of the relativistic motion of bodies endowed with arbitrary multipole structure will be the subject of subsequent publications.read more
Citations
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Journal ArticleDOI
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.
TL;DR: The current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries is presented.
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Tensor-multi-scalar theories of gravitation
TL;DR: In this article, a generic class of theories where gravity is mediated by one tensor field together with an arbitrary number of scalar fields is considered, and the predictions of these theories are worked out in four different observationally relevant regimes.
Journal ArticleDOI
Relativistic tidal properties of neutron stars
Thibault Damour,Alessandro Nagar +1 more
TL;DR: In this paper, the authors study the various linear responses of neutron stars to external relativistic tidal fields and find that the Love number of a star decreases with the radius of the star.
Journal ArticleDOI
The iau 2000 resolutions for astrometry celestial mechanics and metrology in the relativistic framework: explanatory supplement
Michael Soffel,Sergei A. Klioner,Gérard Petit,Peter Wolf,Sergei M. Kopeikin,P. Bretagnon,Victor A. Brumberg,N. Capitaine,Thibault Damour,Toshio Fukushima,B. Guinot,Tian-Yi Huang,Tian-Yi Huang,Lennart Lindegren,C. Ma,Kenneth Nordtvedt,John C Ries,P. K. Seidelmann,David Vokrouhlický,Clifford M. Will,Chong-Yu Xu +20 more
TL;DR: The IAU resolutions B1.3, B 1.4, B1 1.5, and B1 2.9 were adopted during the 24th General Assembly in Manchester, 2000, and provides details on and explanations for these resolutions as discussed by the authors.
IERS Conventions (2010)
Gérard Petit,Brian J. Luzum +1 more
TL;DR: The IERS Conventions (2010) as mentioned in this paper define the standard reference systems realized by the International Earth Rotation and Reference Systems Service (IERS) and the models and procedures used for this purpose.
References
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Journal ArticleDOI
Classical theory of radiating electrons
TL;DR: In this article, the authors argue that the Lorentz model has reached the limit of its usefulness and must be abandoned before we can make further progress in the field of physics.
Journal ArticleDOI
Multipole expansions of gravitational radiation
TL;DR: In this article, a unified notation for the multipole formalisms for gravitational radiation is presented, which includes scalar, vector, and tensor spherical harmonics used in the general relativity literature, including Regge-Wheeler harmonics, the symmetric, trace-free ("STF") tensors of Sachs and Pirani, the Newman-Penrose spin-weighted harmonics and the Mathews-Zerilli Clebsch-Gordan-coupled harmonics.
Journal ArticleDOI
The Gravitational equations and the problem of motion
TL;DR: In this article, it was shown that the relativistic equations of gravitation for empty space are sufficient to determine the motion of matter represented as point singularities of the field.
Journal ArticleDOI
Multipole moments of stationary space-times
TL;DR: In this paper, the mass moments and angular momentum moments are defined for stationary, asymptotically flat, source-free solutions of Einstein's equation and properties of these moments are derived.
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