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
Author(s): Joan Girbau, Lluís Bruna (auth.)
Series: Progress in Mathematical Physics 58
Edition: 1
Publisher: Birkhäuser Basel
Year: 2010
Language: English
Pages: 208
Tags: Partial Differential Equations; Theoretical, Mathematical and Computational Physics
Front Matter....Pages i-xv
Pseudo-Riemannian Manifolds....Pages 1-17
Introduction to Relativity....Pages 19-48
Approximation of Einstein’s Equation by the Wave Equation....Pages 49-62
Cauchy Problem for Einstein’s Equation with Matter....Pages 63-108
Stability by Linearization of Einstein’s Equation, General Concepts....Pages 109-128
General Results on Stability by Linearization when the Submanifold M of V is Compact....Pages 129-147
Stability by Linearization of Einstein’s Equation at Minkowski’s Initial Metric....Pages 149-176
Stability by Linearization of Einstein’s Equation in Robertson-Walker Cosmological Models....Pages 177-200
Back Matter....Pages 201-208
