An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the “outside” is then usually reduced to a scattering process, in which incoming radiation interacts with the system, which in turn emits outgoing radiation.In Einstein’s theory of gravitation, isolated systems are modeled as asymptotically flat spacetimes. They provide the appropriate paradigm for the study of gravitational waves and their interaction with a material system or even only with themselves. In view of the emerging era of gravitational wave astronomy, in which gravitational wave signals from many different astrophysical sources are detected and interpreted, it is necessary to have a foundation for the theoretical and numerical treatments of these signals.Furthermore, from a purely mathematical point of view, it is important to have a full understanding of the implications of imposing the condition of asymptotic flatness onto solutions of the Einstein equations. While it is known that there exists a large class of asymptotically flat solutions of Einstein’s equations, it is not known what the necessary and sufficient conditions at infinity are that have to be imposed on initial data so that they evolve into regular asymptotically flat spacetimes. The crux lies in the region near spacelike infinity [Formula: see text] where incoming and outgoing radiation “meet”.In this paper, we review the current knowledge and some of the analytical and numerical work that has gone into the attempt to understand the structure of asymptotically flat spacetimes near spacelike and null-infinity.

中文翻译：

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探索时空的无限区域

物理学中的一个重要概念是孤立系统的概念。它用于许多不同的领域来描述与环境隔离的物理系统的属性。与“外部”的相互作用通常被简化为散射过程，其中入射辐射与系统相互作用，系统又发射出辐射。在爱因斯坦的万有引力理论中，孤立系统被建模为渐近平坦的时空。它们为研究引力波及其与物质系统甚至仅与自身的相互作用提供了适当的范式。鉴于引力波天文学的新兴时代，来自许多不同天体物理源的引力波信号被检测和解释，有必要为这些信号的理论和数值处理打下基础。此外，从纯数学的角度来看，充分理解将渐近平坦度条件强加于爱因斯坦解的含义是很重要的方程。虽然已知存在一大类爱因斯坦方程的渐近平坦解，但尚不清楚必须对初始数据施加无限远的必要和充分条件，以便它们演变成规则的渐近平坦时空。症结在于接近空间无限的区域[公式：见正文]，输入和输出辐射“相遇”。在本文中，