Generalized pseudo-Riemannian geometry
نویسندگان
چکیده
Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fundamental Lemma of (pseudo-) Riemannian geometry” in this setting and define the notion of geodesics of a generalized metric. Finally, we present applications of the resulting theory to general relativity. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 46F10, 83C05
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