## Noncommutative structure of singularities in general relativity

### Authors:

- Michael Heller,
- Wiesław Sasin

### Abstract

Initial and final singularities in the closed Friedman world model are typical examples of malicious singularities. They form the single point of Schmidt’s b‐boundary of this model and are not Hausdorff separated from the rest of space–time. The method of noncommutative geometry, developed by A. Connes and his co‐workers, is applied to this case. We rephrase Schmidt’s construction in terms of the groupoid of orthonormal frames over space–time and carry out the ‘‘desingularization’’ process. We define the line bundle τ:Ω1/2→ over and change the space of its cross sections into an involutive algebra. This algebra is represented in the space of operators on a Hilbert space and, with the norm inherited from these operators, it becomes a C∗‐algebra. The initial and final singularities of the closed Friedman model are given by two distinct representations of this C∗‐algebra in the space of operators acting on the Hilbert space L2(O(3,1)). © 1996 American Institute of Physics.

- Record ID
- WUT113588
- Author
- Journal series
- Journal of Mathematical Physics, ISSN 00222488
- Issue year
- 1996
- Vol
- 37
- No
- 11
- Pages
- 5665-5671
- DOI
- DOI:10.1063/1.531733 Opening in a new tab
- URL
- http://jmp.aip.org/resource/1/jmapaq/v37/i11/p5665_s1 Opening in a new tab
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 13; = 22
- Citation count
- 22

- Uniform Resource Identifier
- https://repo.pw.edu.pl/info/article/WUT113588/

- URN
`urn:pw-repo:WUT113588`

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.