Geodesic
The closed Friedman world model with the initial and final singularities as a non-commutative space
Banach Center Publications, Tome 41 (1997) no. 1, pp. 153-161.

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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.
DOI : 10.4064/-41-1-153-161
Keywords: singularities, Friedman cosmology, non-commutative geometry

Michael Heller 1 ; Wiesław Sasin 1

1 
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Michael Heller; Wiesław Sasin. The closed Friedman world model with the initial and final singularities as a non-commutative space. Banach Center Publications, Tome 41 (1997) no. 1, pp. 153-161. doi : 10.4064/-41-1-153-161. http://geodesic.mathdoc.fr/articles/10.4064/-41-1-153-161/

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