On Lorentz geometry in algebras of generalized functions

Eberhard Mayerhofer

doi:10.1017/S0308210506000898

On Lorentz geometry in algebras of generalized functions

Eberhard Mayerhofer

University of Vienna

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	843-871
Number of pages	29
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	138
Issue number	4
DOIs	https://doi.org/10.1017/S0308210506000898
Publication status	Published - Aug 2008
Externally published	Yes

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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.",

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On Lorentz geometry in algebras of generalized functions

Abstract

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