On Lorentz geometry in algebras of generalized functions
Eberhard Mayerhofer
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.
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