Weak-field approximation of a scalar theory of gravitation and some remarks on the propagation effects of gravity

TL;DR

This paper explores the weak-field limit of a scalar gravitation theory using asymptotic expansions, showing that only the post-Newtonian approach aligns with Newtonian physics and that no propagation effects appear up to second order.

Contribution

It demonstrates the applicability of asymptotic expansion methods to scalar gravitation theories and clarifies the limitations regarding propagation effects at low orders.

Findings

Only the post-Newtonian expansion is compatible with the Newtonian limit.

No non-Newtonian or propagation effects are observed up to order 1/c^2.

The method is general and applicable to other weak-field gravitational models.

Abstract

A simple example is given of the implementation of the usual method of asymptotic expansions for weak gravitational fields. A scalar, preferred-frame theory of gravitation is considered, but the method is general. Two kinds of asymptotic expansion are a priori possible: "post-Newtonian" (PN) or "post-Minkowskian", the latter allowing to account directly for propagation effects. However, it is shown that only the PN asymptotic expansion is compatible with the Newtonian limit. It is also shown that, in the scalar theory, there is no non-Newtonian effect (in particular, no propagation effect) up to the second order, i.e., the order 1/c^2.