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Point-particle limit in a scalar theory of gravitation and the weak equivalence principle

Mayeul Arminjon
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Abstract

A scalar theory with a preferred reference frame is summarized. To test that theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has been developed. This associates a conceptual family of self-gravitating systems with the given system, in order to have a true small parameter available. The resulting equations for a weakly-self-gravitating system of extended bodies include internal-structure effects. The internal-structure influence subsists at the point-particle limit--a violation of the weak equivalence principle. If one could develop an "asymptotic" approximation scheme in general relativity also, this could plausibly be found there also, in a gauge where the PN space metric would not be "conformally Euclidean".

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Mayeul Arminjon. 2003-06-06. Point-particle limit in a scalar theory of gravitation and the weak equivalence principle. https://arxiv.org/abs/gr-qc/0306025

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