Generalized pseudo-Riemannian geometry

Michael Kunzinger; Roland Steinbauer

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Generalized pseudo-Riemannian geometry

Michael Kunzinger·Roland Steinbauer

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Abstract

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.

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Michael Kunzinger, Roland Steinbauer. 2002-10-31. Generalized pseudo-Riemannian geometry. https://arxiv.org/abs/math/0107057

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