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Abstract：
This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic set-ups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we will obtain in upcoming work. From the physical perspective, this includes a discussion of how post-Newtonian theory provides a prediction on the gravitational radiation emitted by [Formula: see text] infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from [Formula: see text], as a starting point to set up a scattering problem for the linearized Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near [Formula: see text] and [Formula: see text]. The full mathematical details will be presented in the sequel to this paper. This article is part of a discussion meeting issue \'At the interface of asymptotics, conformal methods and analysis in general relativity\'.
摘要：
本文是致力于在天体物理现实设置下对引力辐射进行数学上严格的渐近分析的系列文章中的第四篇。它概述了设置数学问题所涉及的物理思想，一旦问题提出，需要克服的数学挑战，以及我们将在即将开展的工作中获得的主要新成果。从物理角度来看,这包括对后牛顿理论如何提供对[公式：见文字]从中间区域无限过去的质量中发射的引力辐射的预测的讨论，即达到一些有限的先进时间。从数学的角度来看,然后我们接受这个预测，加上没有来自[公式：见正文]的入射辐射的条件，作为为Schwarzschild和近似空间无穷大的线性化爱因斯坦真空方程建立散射问题的起点，并概述了如何解决此散射问题，并获得[公式：见文本]和[公式：见文本]附近的散射解的渐近性质。完整的数学细节将在本文的续集中介绍。这篇文章是讨论会议问题的一部分，在渐近性的界面上，广义相对论中的共形方法和分析。
