Weak-field approximation of a scalar theory of gravitation and some remarks on the propagation effects of gravity
Abstract
Description
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.
15 pages, HTML. In the previous version, the author believed to have found a post-Minskowskian approximation which was consistent with both the usual method of asymptotic expansions and the Newtonian limit. It is now shown that only the post-Newtonian approximation with instantaneous propagation meets these two requirements, and the mistake that was done is pointed out. Method and main conclusion unchanged: no non-Newtonian effect before 1/c^2. One reference added
15 pages, HTML. In the previous version, the author believed to have found a post-Minskowskian approximation which was consistent with both the usual method of asymptotic expansions and the Newtonian limit. It is now shown that only the post-Newtonian approximation with instantaneous propagation meets these two requirements, and the mistake that was done is pointed out. Method and main conclusion unchanged: no non-Newtonian effect before 1/c^2. One reference added