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.
@article{bwmeta1.element.bwnjournal-article-bcpv41z1p153bwm,
author = {Heller, Michael and Sasin, Wies\l aw},
title = {The closed Friedman world model with the initial and final singularities as a non-commutative space},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {153-161},
zbl = {0887.53062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p153bwm}
}
Heller, Michael; Sasin, Wiesław. The closed Friedman world model with the initial and final singularities as a non-commutative space. Banach Center Publications, Tome 38 (1997) pp. 153-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p153bwm/
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