Noncommutative structure of singularities in general relativity
- University of Liege, Institute of Astrophysics, Avenue de Cointe 5, B-4000 Liege (Belgium)
- Institute of Mathematics, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw (Poland)
Initial and final singularities in the closed Friedman world model are typical examples of {ital malicious} singularities. They form the single point of Schmidt{close_quote}s {ital b}-boundary of this model and are not Hausdorff separated from the rest of space{endash}time. The method of noncommutative geometry, developed by A. Connes and his co-workers, is applied to this case. We rephrase Schmidt{close_quote}s construction in terms of the groupoid {bar {ital G}} of orthonormal frames over space{endash}time and carry out the {open_quote}{open_quote}desingularization{close_quote}{close_quote} process. We define the line bundle {tau}:{Omega}{sup 1/2}{r_arrow}{bar {ital G}} over {bar {ital G}} 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 {ital C}{asterisk}-algebra. The initial and final singularities of the closed Friedman model are given by two distinct representations of this {ital C}{asterisk}-algebra in the space of operators acting on the Hilbert space {ital L}{sup 2}{bold (}{ital O}(3,1){bold )}. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 388203
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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