标题： 相对论天体力学的渐近展开 显示英文标题

标题： Asymptotic expansions for relativistic celestial mechanics

摘要： 使用渐近展开的方法，构建了与相对论引力理论中的天体力学相关的近似方案。 一种标量理论被考虑，既作为简单的例子，也因其自身的重要性。 该理论被总结后，相关边界问题被看作是完整的初始值问题。 表明，对于任何给定的引力物体系统，可以关联一个单参数的相似系统，该参数衡量引力场的强度。 在进行特定单位变换后，渐近展开的推导变得直接。 可以做出两种假设，以确定在展开中应使用哪种时间变量。 第一种假设导致一种“渐近”的后牛顿近似（PNA），具有瞬时传播，与标准的PNA不同，在渐近PNA中，所有场都被展开。 第二种假设可能导致一种“渐近”的后闵可夫斯基近似（PMA），允许描述传播效应，但它与牛顿极限不兼容。 表明，标准的PNA与此处设想的通常渐近展开方法的应用不兼容。 显示英文摘要

摘要： The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem. It is shown that, with any given system of gravitating bodies, one may associate a one-parameter family of similar systems, the parameter measuring the gravitational field-strength. After a specific change of units, the derivation of asymptotic expansions becomes straightforward. Two hypotheses could be made as to which time variable has to be used in the expansion. The first one leads to an "asymptotic" post-Newtonian approximation (PNA) with instantaneous propagation, differing from the standard PNA in that, in the asymptotic PNA, all fields are expanded. The second hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA) allowing to describe propagation effects, but it is not compatible with the Newtonian limit. It is shown that the standard PNA is not compatible with the application of the usual method of asymptotic expansions as envisaged here.