Generalized pseudo-Riemannian geometry |
| |
Authors: | Michael Kunzinger Roland Steinbauer |
| |
Affiliation: | Department of Mathematics, University of Vienna, Strudlhofg. 4, A-1090 Wien, Austria ; Department of Mathematics, University of Vienna, Strudlhofg. 4, A-1090 Wien, Austria |
| |
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. |
| |
Keywords: | Algebras of generalized functions Colombeau algebras generalized tensor fields generalized metric (generalized) pseudo-Riemannian geometry general relativity. |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Transactions of the American Mathematical Society》下载全文 |