Addendum to ‘‘Classical and quantum evolutions of the de Sitter and the anti–de Sitter universes in 2+1 dimensions’’
Open accessAbstract
The discussion in a previous paper on reducing the phase space of the first-order Einstein gravity in 2+1 dimensions is refined. We provide a prescription to construct a ``correct'' physical phase space in the case of a positive cosmological constant. A parametrization which unifies the two sectors of the physical phase space is also given. Unlike the cases of a nonpositive cosmological constant, the unified phase space turns out to be Hausdorff type when the cosmological constant is positive.
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An explicit example of the ambiguity for de Sitter structures has been given by Ezawa for the topology R×T2.
“An explicit example of the resulting ambiguity has been given by Ezawa [117] for the case of a topology ℝ × T2”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [117]
Only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike.
“It may be shown that only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike [117, 119, 182, 209].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [117]
The discussion on p. 2 identifies standard and flat sectors for torus spatial hypersurfaces. On p. 4, the paper compares its standard sector with a spacelike sector in the Λ = 0 case, but it does not say that only a hyperbolic-hyperbolic sector permits spacelike T² slices. Searches for the hyperbolic-hyperbolic sector and the causal character of torus slices found no passage establishing the claim. (LLM, conf=0.74)
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Research works printed but not linked: 5
- [1][1] K. Ezawa, preprint OU-HET/183, hep-th/9311103, to appear in Phys. Rev. D. - · arXiv
- [5][5] G. Mess, preprint IHES/M/90/28. -
- [8][8] J. Louko and D. M. Marolf, preprint SU-GP-93/7-6, gr-qc/9308018. - · arXiv
- [9][9] K. Ezawa, preprint OU-HET/185, hep-th/9312151. - · arXiv
- [11][11] A. Ashtekar, Lectures on Non-perturbative Canonical Gravity (World Scientific, Singapore 1991).
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Ezawa, K.
- Affiliations
- The University of Osaka (JP)
- Corresponding author
- Ezawa, Kiyoshi
- ORCID
- Ezawa, Kiyoshi
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1994-08-15
- Volume
- 50
- Issue
- 4
- Pages
- 2935-2938
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2134152825
- Cited by
- 7
- References
- 0
- FWCI
- 2.42
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- three-dimensional gravity, phase space reduction, de Sitter universe, positive cosmological constant, quantum evolution
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