The Cauchy Problem in General Relativity.

Format:

Book

Author/Creator:

Ringström, Author.

Series:

ESI Lectures in Mathematics and Physics (esi) 2943-4939 6

Language:

English

Physical Description:

1 online resource (307 pages)

Place of Publication:

EMS Press 2009

System Details:

text file PDF

Summary:

The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einsteins equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaître-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einsteins equations as an initial value problem allows a closer study of their solutions. 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 fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

ISBN:

3-03719-553-3