Differential groupoids and their application to the theory of spacetime singularities
type: Item
instance of: scholarly article
title: Differential groupoids and their application to the theory of spacetime singularities
zbMATH Open document ID: 0996.83037
DOI: 10.1023/A:1015745226298
author: Wiesław Sasin
author: Michal P. Heller
published in: International Journal of Theoretical Physics
publication date: 2002-07-09T00:00:00Z
review text: The spacetime singularities are studied by using the concept of differential groupoid (DG) in the category of structured spaces. The DG is represented by an algebra of operators on a bundle of Hilbert spaces defined on the groupoid fibers. It is shown that any spacetime with singularities can be regarded as a noncommutative space. Information on a given singularity is obtained from the isotropy group of the ``singular fiber''. This group is thought as measuring the ``strength'' of the singularity. Different properties are reflected in the structure of the representation of the corresponding DG in a Hilbert space and, to some extent, in a noncommutative algebra defined on this groupoid. Some illustrative examples, showing the ``desingularization'' process, are given.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 83C75
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 81R60
zbMATH DE Number: 1765095
zbMATH Keywords: spacetime singularity
zbMATH Keywords: differential groupoid
zbMATH Keywords: structured space
zbMATH Keywords: singular fiber
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1765095