This paper is about two important trends of scattering theory in general relativity: time-dependent spectral analytic scattering and conformal scattering. The former was initiated by Jonathan Dimock and Bernard Kay in the mid-1980s and is based on spectral and functional analysis. The latter was proposed by Roger Penrose in 1965 and then constructed for the first time by Gerard Friedlander in 1980 by putting together Penrose’s conformal method and another analytic approach to scattering: the Lax–Phillips theory due to Peter Lax and Ralph Phillips. We shall review the history of the two approaches and explain their general principles. We shall also explore an important question: ‘can the tools of one approach be used to obtain a complete construction in the other?’ 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：

---

广义相对论中的解析散射和共形散射

本文讨论了广义相对论中散射理论的两个重要趋势：依赖于时间的光谱分析散射和共形散射。前者由 Jonathan Dimock 和 Bernard Kay 在 20 世纪 80 年代中期发起，基于光谱和泛函分析。后者由罗杰·彭罗斯 (Roger Penrose) 于 1965 年提出，然后由杰拉德·弗里德兰德 (Gerard Friedlander) 于 1980 年首次构建，将彭罗斯的保角方法和另一种散射分析方法结合在一起：彼得·拉克斯 (Peter Lax) 和拉尔夫·菲利普斯 (Ralph Phillips) 提出的 Lax-Phillips 理论。我们将回顾这两种方法的历史并解释它们的一般原理。我们还将探讨一个重要问题：“一种方法的工具可以用来获得另一种方法的完整构造吗？” 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。