Stability by Linearization of Einstein's Field Equation

1. Front Matter

   Pages i-xv

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2. Pseudo-Riemannian Manifolds

   • Joan Girbau, Lluís Bruna

   Pages 1-17

3. Introduction to Relativity

   • Joan Girbau, Lluís Bruna

   Pages 19-48

4. Approximation of Einstein’s Equation by the Wave Equation

   • Joan Girbau, Lluís Bruna

   Pages 49-62

5. Cauchy Problem for Einstein’s Equation with Matter

   • Joan Girbau, Lluís Bruna

   Pages 63-108

6. Stability by Linearization of Einstein’s Equation, General Concepts

   • Joan Girbau, Lluís Bruna

   Pages 109-128

7. General Results on Stability by Linearization when the Submanifold M of V is Compact

   • Joan Girbau, Lluís Bruna

   Pages 129-147

8. Stability by Linearization of Einstein’s Equation at Minkowski’s Initial Metric

   • Joan Girbau, Lluís Bruna

   Pages 149-176

9. Stability by Linearization of Einstein’s Equation in Robertson-Walker Cosmological Models

   • Joan Girbau, Lluís Bruna

   Pages 177-200

10. Back Matter

    Pages 201-208

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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

• 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
• partial differential equations

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)

• Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

  Joan Girbau, Lluís Bruna

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