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

Banach Center Publications (1997)

- Volume: 41, Issue: 1, page 153-161
- ISSN: 0137-6934

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topHeller, Michael, and Sasin, Wiesław. "The closed Friedman world model with the initial and final singularities as a non-commutative space." Banach Center Publications 41.1 (1997): 153-161. <http://eudml.org/doc/252197>.

@article{Heller1997,

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.},

author = {Heller, Michael, Sasin, Wiesław},

journal = {Banach Center Publications},

keywords = {singularities; Friedman cosmology; non-commutative geometry; closed Friedman model; -boundary points},

language = {eng},

number = {1},

pages = {153-161},

title = {The closed Friedman world model with the initial and final singularities as a non-commutative space},

url = {http://eudml.org/doc/252197},

volume = {41},

year = {1997},

}

TY - JOUR

AU - Heller, Michael

AU - Sasin, Wiesław

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

JO - Banach Center Publications

PY - 1997

VL - 41

IS - 1

SP - 153

EP - 161

AB - 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.

LA - eng

KW - singularities; Friedman cosmology; non-commutative geometry; closed Friedman model; -boundary points

UR - http://eudml.org/doc/252197

ER -

## References

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