EMS ESI Lectures in Mathematics and Physics
Volume: 6; 2009; 307 pp; Softcover
MSC: Primary 83;
Print ISBN: 978-3-03719-053-1
Product Code: EMSESILEC/6
List Price: $58.00
Individual Member Price: $46.40
The Cauchy Problem in General RelativityShare this page
A publication of the European Mathematical Society
The general theory of relativity is a theory of manifolds equipped
with Lorentz metrics and fields which describe the matter content. Einstein's
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
modelling an isolated system and the entire universe respectively. In a
different approach, formulating
Einstein's equations as an initial value problem allows a closer study of
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 without prior background in 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.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Table of Contents
Table of Contents
The Cauchy Problem in General Relativity
Graduate students and research mathematicians interested in mathematical physics.