On Lorentz geometry in algebras of generalized functions
Mathematical Physics
2009-10-09 v3 math.MP
Rings and Algebras
Abstract
We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. 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 in Hawking and Ellis's book "The large scale structure of space-time". Our work is based on a new characterization of free elements in finite dimensional modules over the ring of generalized numbers.
Cite
@article{arxiv.math-ph/0604052,
title = {On Lorentz geometry in algebras of generalized functions},
author = {Eberhard Mayerhofer},
journal= {arXiv preprint arXiv:math-ph/0604052},
year = {2009}
}
Comments
26 pages, reorganized, updated references