Conformal Methods in General Relativity (Paperback)

This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this an ideal reference companion on the topic. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.

本書系統地介紹了共形方法及其如何應用於研究愛因斯坦引力理論方程的解的全局性質。它展示了將這些思想與微分幾何相結合可以闡明該理論的基本解的存在性和穩定性。本書介紹了獲得對共形方法深入理解所需的微分幾何、旋量和偏微分方程背景，提供了過去三十年數學相對論中的關鍵結果的易於理解的描述，包括de Sitter和Minkowski時空的穩定性。對於研究生和研究人員來說，本書是一個自包含的資源，包括有助於讀者理解抽象概念的視覺模型和進一步閱讀的列表，是該主題的理想參考資料。本書於2016年首次出版，現已作為開放存取出版物重新發行在Cambridge Core上。