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© 2010

Stability by Linearization of Einstein’s Field Equation

Book

Part of the Progress in Mathematical Physics book series (PMP, volume 58)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Joan Girbau, Lluís Bruna
    Pages 1-17
  3. Joan Girbau, Lluís Bruna
    Pages 19-48
  4. Joan Girbau, Lluís Bruna
    Pages 49-62
  5. Joan Girbau, Lluís Bruna
    Pages 63-108
  6. Back Matter
    Pages 201-208

About this book

Introduction

V ? V ?K? , 3 2 2 R ? /?x K i i g V T G g ?T , ? G g g 4 ? R ? ? G ? T g g ? h h ? 2 2 2 2 ? ? ? ? ? ? ? h ?S , ?? ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? T?. ? ˜ T S 2 2 2 2 ? ? ? ? ? ? ? h . ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? X M ×X M ?? X M X,Y ?? Y X ? Y ? Y ? Y X +X X X 1 2 1 2 ? Y Y ? Y ? Y X 1 2 X 1 X 2 ? Y f? Y f?F M fX X ? fY X f Y f? Y f?F M X X ? torsion ? Y?? X X,Y X,Y?X M . X Y localization principle Theorem I.1. Let X, Y, X , Y be C vector ?elds on M.Let U be an open set

Keywords

Cauchy problem for Einstein’s equation EFE Einstein's equation Gravity Pseudo-Riemannian manifolds Relativity Robertson-Walker models Sobolev spaces Special relativity Stability by linearization general relativity

Authors and affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain

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Reviews

From the reviews:

“The authors of the book under review have contributed to this subject over the last ten years by studying the linearization stability for Einstein’s equations with source terms and in cosmological solutions. Here they present the results in a systematic fashion accessible to a reader with some background in differential geometry and partial differential equations.” (Hans-Peter Künzle, Mathematical Reviews, Issue 2011 h)