The Cauchy problem in general relativity.
type: Item
instance of: scholarly article
title: The Cauchy problem in general relativity.
zbMATH Open document ID: 1169.83003
DOI: 10.4171/053
author: Hans Ringström
published in: ESI Lectures in Mathematics and Physics
publication date: 2009-06-11T00:00:00Z
review text: This monograph deals with almost all aspects of the Cauchy problem in general relativity, starting with a short historical overview, and inserting almost all necessary ingredients: from the theory of partial differential equations, differential geometry and relativity theory. Appendices list several notions and conventions used in the book, bibliography and index are quite useful, too. Unfortunately, only very few figures are given even for such parts of the material, where they would be quite helpful, and are usually given in other literature on the topic. Part I gives the background from the theory of partial differential equations, like Fourier transforms, Sobolov space, and wave equations. Part II presents the Lorentz geometry background, especially the notion of global hyperbolicity. Part III covers the constraint equation, local existence, Cauchy stability and the existence of a maximal globally hyperbolic development for the Einstein equation. Part IV titles ``Pathologies, strong cosmic censorship'', and is an example of the proverb ``A good theory lives from its counterexamples.'', in this case it means a lot of examples which contradict every-day experience, like the non-uniqueness of the possible maximal extensions of given initial data. Another example is the closed universe recollapse conjecture. From the Publisher's description: ``This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those wishing to enter the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the…
reviewed by: Hans-Jürgen Schmidt
Mathematics Subject Classification ID: 83-02
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 83A05
Mathematics Subject Classification ID: 83C25
Mathematics Subject Classification ID: 83C75
Mathematics Subject Classification ID: 83C15
Mathematics Subject Classification ID: 83F05
zbMATH DE Number: 5564123
zbMATH Keywords: strong cosmic censorship
zbMATH Keywords: Cauchy problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/053
OpenAlex ID: W4300641598
description: scientific article; zbMATH DE number 5564123