On Lorentz geometry in algebras of generalized functions
Published online by Cambridge University Press: 28 July 2008
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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