Stability by Linearization of Einstein's Field Equation

, 3 2 2 R ? /?x K i i g V T G g ?T , ? 2 2 2 2 ? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? ~ T S 2 2 2 2 ? 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 ? Y X +X X X 1 2 1 2 ? Y X 1 2 X 1 X 2 ?