Motion of the mass centers in a scalar theory of gravitation: the point particle limit

PDF, 22 pages. v3: Magnitude of the WEP violation for the Pioneer spacecrafts estimated more precisely (Sect. 6). Result: anisotropic-metric version of the scalar theory discarded (Conclusion). Former Sect. 2 suppressed, new references added. v2: minor corrections on pp. 10, 12 and 14We 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 schem