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On Lorentz geometry in algebras of generalized functions

Published online by Cambridge University Press:  28 July 2008

Eberhard Mayerhofer
Eberhard Mayerhofer
Affiliation:
Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria ([email protected])
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Abstract

We introduce the concept of causality into the framework of generalized pseudo-Riemannian geometry in the sense of Colombeau and establish the inverse Cauchy–Schwarz inequality in this context. As an application, we prove a dominant energy condition for some energy tensors as put forward by Hawking and Ellis. Our work is based on a new characterization of free elements in finite-dimensional modules over the ring of generalized numbers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 4 , August 2008 , pp. 843 - 871
Copyright
2008 Royal Society of Edinburgh

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