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1997 | 41 | 1 | 153-161
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
41
Numer
1
Strony
153-161
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Vatican Observatory, V-12000 Vatican City State
  • Institute of Mathematics, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland
Bibliografia
  • [1] R. L. Bishop and S. I. Goldberg, Tensor Analysis on Manifolds, Dover, New York, 1968.
  • [2] B. Bosshard, On the b-boundary of the closed Friedman model, Commun. Math. Phys. 46 (1976), 263-268.
  • [3] A. Connes, in: Algèbres d'opérateurs, Lecture Notes in Mathematics, no 725, P. de la Harpe (ed.), Springer, Heidelberg - Berlin - New York 1979.
  • [4] A. Connes, Noncommutative Geometry, Academic Press, New York, 1994.
  • [5] J. Dixmier, Les C*-algèbres et leur représentations, Gauthier-Villars, Paris, 1969.
  • [6] J. Gruszczak and M. Heller, Differential structure of space-time and its prolongations to singular boundaries, Intern. J. Theor. Phys. 32 (1993), 625-648.
  • [7] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1973.
  • [8] M. Heller, P. Multarzyński, W. Sasin and Z. Żekanowski, On some generalizations of the manifold concept, Acta Cosmologica 18 (1992), 31-44.
  • [9] M. Heller and W. Sasin, The structure of the b-boundary of space-time, Gen. Rel. Grav. 26 (1994), 797-811.
  • [10] M. Heller and W. Sasin, Sheaves of Einstein algebras, Int. J. Theor. Phys. 34 (1995), 387-398.
  • [11] M. Heller and W. Sasin, Structured spaces and their application to relativistic physics, J. Math. Phys. 36 (1995), 3644-3662.
  • [12] M. Heller, W. Sasin, A. Trafny and Z. Żekanowski, Differential spaces and new aspects of Schmidt's b-boundary of space-time, Acta Cosmologica 18 (1992), 57-75.
  • [13] R. A. Johnson, The bundle boundary in some special cases, J. Math. Phys. 18 (1977), 898-902.
  • [14] J. L. Koszul, Fibre bundles and differential geometry, Tata Institute of Fundamental Research, Bombay, 1960.
  • [15] J. Madore, An Introduction to Noncommutative Differential Geometry and Its Physical Applications, Cambridge University Press, Cambridge, 1995.
  • [16] G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, Boston - New York - London, 1990.
  • [17] J. Renault, A groupoid approach to C*-algebras, Lecture Notes in Math. 793, Springer, Berlin - Heidelberg - New York, 1980.
  • [18] W. Sasin, Differential spaces and singularities in differential space-times, Demonstratio Mathematica 24 (1991), 601-634.
  • [19] W. Sasin and M. Heller, Space-time with b-boundary as a generalized differential space, Acta Cosmologica 19 (1993), 35-44.
  • [20] B. G. Schmidt, A new definition of singular points in general relativity, Gen. Rel. Grav. 1 (1971), 269-280.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv41z1p153bwm
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