Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-01-09
Romanian Journal of Physics, Volume 49, Numbers 7-8, 2004, pp. 549 - 572
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
PDF, 22 pages. v3: Magnitude of the WEP violation for the Pioneer spacecrafts estimated more precisely (Sect. 6). Result: anis
Scientific paper
We investigate the point-particle limit of the equations of motion valid for a system of extended bodies in a scalar alternative theory of gravitation: the size of one of the bodies being a small parameter xi, we calculate the limit, as xi tends towards 0, of the post-Newtonian (PN) acceleration of this small body. We use the asymptotic scheme of PN approximation, that expands all fields. We find that the PN acceleration A of the small body keeps a structure-dependent part at this limit. In particular, if the only massive body is static and spherical, then A differs from the PN acceleration of a test particle in a Schwarzschild field only by this structure-dependent part. The presence of the latter is due to the fact that the PN metric depends on the first spatial derivatives of the Newtonian potential. Since just the same form of PN metric is valid for the standard form of Schwarzschild's solution, the acceleration of a small body might keep a structure-dependent part at the point limit in general relativity also, depending on the gauge. The magnitude of the structure-dependent acceleration is already challenging on Earth. For the Pioneer spacecrafts, it is likely to discard the current version of the scalar theory. A modified version has been outlined in a quoted reference. Keywords: Weak equivalence principle violation, Asymptotic post-Newtonian scheme
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