On Lorentz geometry in algebras of generalized functions

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...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 138; no. 4; pp. 843 - 871
Main Author Mayerhofer, Eberhard
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.08.2008
Cambridge University Press
Subjects
Algebra
Geometry
Mathematics
Partial differential equations
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Summary: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.
Bibliography:PII:S0308210506000898
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content type line 23
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210506000898