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 N 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 I − , 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 i 0 and I + . 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’.

中文翻译：

---

反对平滑零无穷大的案例 IV：史瓦西周围的线性重力——概述

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严格渐近分析的系列文章中的第四篇。它概述了建立数学问题所涉及的物理思想、提出问题后需要克服的数学挑战，以及我们在接下来的工作中将获得的主要新成果。从物理角度来看，这包括讨论后牛顿理论如何预测引力辐射 氮 来自无限过去的坠落群众在中间区，即达到某个有限的提前时间。从数学的角度来看，我们然后进行这个预测，以及没有来自任何地方的入射辐射的条件 我 - ，作为建立史瓦西附近和类空间无穷大附近的线性化爱因斯坦真空方程的散射问题的起点，我们概述了如何解决这个散射问题并获得附近的散射解的渐近性质 我 0 和 我 + 。完整的数学细节将在本文的后续部分中介绍。本文是讨论会议问题“渐进、共形方法和广义相对论分析的接口”的一部分。