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Zbl 1136.83001
Christodoulou, Demetrios
Mathematical problems of general relativity. I. (English)
[B] Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society (EMS). x, 147~p. EUR~28.00 (2008). ISBN 978-3-03719-005-0/pbk

This book is based on lectures read by its author at Eidgenossische Hochschule Zürich in 2003. Its title is not very precise, because it contains mainly a lot of material about the vacuum solutions of the Einstein field equation in the asymptotically flat case; only at some places, also an electromagnetic field and a scalar field are added as sources. And within this class of topics, the main emphasis, see chapter 4, is on the global stability of Minkowski spacetime. The introduction is quite short, in principle the reader is assumed to know already the main parts of general relativity. In chapter 2, the Cauchy problem for the Einstein field equation is presented, and in chapter 3, several variants of asymptotic flatness are introduced, conserved quantities, and the Noether theorem are presented, too. The stability result is not completely proved, but the main ideas are given which include conformal transformations, Bianchi identities, and minimal surfaces. The book ends with a short reference list and an index.
[Hans-Jürgen Schmidt (Potsdam)]

MSC 2000:: *83-02 Research monographs (relativity)
83C05 Einstein's equations
35L70 Second order nonlinear hyperbolic equations
53C50 Lorentz manifolds, manifolds with indefinite metrics
35Q75 PDE in relativity
58J45 Hyperbolic equations
83C40 Groups of motions, etc.

Keywords: global stability

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