探索无限的时空区域
Explorations of the infinite regions of space-time
摘要：
物理学中的一个重要概念是孤立系的概念。它在许多不同的领域被用来描述一个与其环境隔离的物理系统的性质。与“外部”的相互作用通常被简化为散射过程，在这个过程中，入射辐射与系统相互作用，系统又发射出辐射。在爱因斯坦的引力理论中，孤立系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例。鉴于引力波天文学的出现，其中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的基础。此外，从纯数学的角度来看，重要的是要充分理解将渐近平坦性条件强加给爱因斯坦方程的解的含义。虽然已知爱因斯坦方程存在一大类渐近平坦解，但不知道在无穷远处必须对初始数据施加什么必要和充分条件，以便它们演化为正则渐近平坦时空。问题的关键在于类空无穷远$i^0$附近的区域，在那里，入射和出射的辐射“相遇”。在本文中，我们回顾了目前的知识和一些分析和数值计算的工作，已经进入试图了解结构的渐近平坦的时空附近的类空和零无限。
英文摘要：
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 space-times. 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 space-times. The crux lies in the region near space-like infinity $i^0$ 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 space-times near space-like and null-infinity.
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