2000/04/18 by Waseem Kamleh, Kamleh, Waseem
Arts and Humanities · Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Philosophy and History of Science #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0004057
19 pages; Section on point-values has been changed, other related and minor changes; Conclusion and focus are essentially the same
openalex publication_date 2000/04/18 · arxiv created 2000/09/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A signature changing spacetime is one where an initially Riemannian manifold with Euclidean signature evolves into the Lorentzian universe we see today. This concept is motivated by problems in causality implied by the isotropy and homogeneity of the universe. As initially time and space are indistinguishable in signature change, these problems are removed. There has been some dispute as to the nature of the junction conditions across the signature change, and in particular, whether or not the metric is continuous there. We determine to what extent the Colombeau algebra of new generalised functions resolves this dispute by analysing both types of signature change within its framework. A covariant formulation of the Colombeau algebra is used, in which the usual properties of the new generalised functions are extended. We find that the Colombeau algebra is insufficient to preclude either continuous or discontinuous signature change, and is also unable to settle the dispute over the nature of the junction conditions.