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ArticleOriginal scientific text

Title

The closed Friedman world model with the initial and final singularities as a non-commutative space

Authors 1, 2

Affiliations

  1. Vatican Observatory, V-12000 Vatican City State
  2. Institute of Mathematics, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

Abstract

The most elegant definition of singularities in general relativity as b-boundary points, when applied to the closed Friedman world model, leads to the disastrous situation: both the initial and final singularities form the single point of the b-boundary which is not Hausdorff separated from the rest of space-time. We apply Alain Connes' method of non-commutative geometry, defined in terms of a C*-algebra, to this case. It turns out that both the initial and final singularities can be analysed as representations of the C*-algebra in a Hilbert space. The method does not distinguish points in space-time, but identifies space slices of the closed Friedman model as states of the corresponding C*-algebra.

Keywords

ENG
singularities, Friedman cosmology, non-commutative geometry

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Banach Center Publications
1997/41/1
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Pages:
153-161
Main language of publication
English
Published
1997
Exact and natural sciences