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

Tom 41 / 1997

Michael Heller, Wiesław Sasin Banach Center Publications 41 (1997), 153-161 DOI: 10.4064/-41-1-153-161


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.


  • Michael Heller
  • Wiesław Sasin

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