Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.084002· OSTI ID:20713723

Arminjon, Mayeul ^[1]

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1. Laboratoire 'Sols, Solides, Structures', CNRS/Universite Joseph Fourier/Institut National Polytechnique de Grenoble, BP 53, F-38041 Grenoble cedex 9 (France)

The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase and Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg's (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter {eta}, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order {eta}{sup 3} included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as {eta}{yields}0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.

• OSTI ID: 20713723
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCELERATION
CORRECTIONS
COSMOLOGY
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS OF MOTION
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL FIELDS
IDEAL FLOW
METRICS
MOMENT OF INERTIA
SPHERICAL CONFIGURATION
SPIN
SYMMETRY