The Effacing Principle in the Post-Newtonian Celestial Mechanics

Details The Effacing Principle in the Post-Newtonian Celestial Mechanics The Effacing Principle in the Post-Newtonian Celestial Mechanics

2006-12-02

arxiv.org/abs/gr-qc/0612017v1

Proc. 11th Marcel Grossmann Meeting, Eds. H. Kleinert, R.T. Jantzen, R. Ruffini. part C, pp. 2475-2477 (Singapore: World Scien

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages, to apper in Proc. of 11th Marcel Grssmann Meeting (Berlin, July 23-30, 2006)

Scientific paper

First post-Newtonian (PN) approximation of the scalar-tensor theory of gravity is used to discuss the effacing principle in N-body system, that is dependence of equations of motion of spherically-symmetric bodies comprising the system on their internal structure. We demonstrate that the effacing principle is violated by terms which are proportional to the second order rotational moment of inertia of each body coupled with \beta-1, where \beta is the measure of non-linearity of gravitational field. In case of general relativity, where \beta=1, the effacing principle is violated by terms being proportional to the rotational moment of inertia of the forth order. For systems made of neutron stars (NS) and/or black holes (BH) these terms contribute to the orbital equations of motion at the level of the third and fifth PN approximation respectively.

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