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Contains classical results on stability of great beauty
Presents the objects needed to prove the theorems and the Cauchy problem for Einstein's equation in a self-contained way
Provides introductory chapters on pseudo-Riemannian manifolds and relativity (both special and general) addressed to readers having no background in these topics and a new definition of stability of Einstein's equation adapted to the case of matter and gives results concerning stability in Robertson-Walker models
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
Content Level »Research
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