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