The solution space of 2 + 1 gravity on in Witten's connection formulation
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We investigate the space of classical solutions of Witten's formulation of 2+1 gravity on the manifold . is connected, unlike the spaces of classical solutions in the cases where is replaced by a higher genus surface. Although is neither Hausdorff nor a manifold, removing from a set of measure zero yields a manifold which is naturally viewed as the cotangent bundle over a non-Hausdorff base space . We discuss the relation of the various parts of with spacetime metrics, and various possibilities of quantizing . There exist quantizations in which the exponentials of certain momentum operators, when operating on states whose support is entirely on the part of corresponding to conventional spacetime metrics, give states whose support is entirely outside this part of . Similar results hold when the gauge group is replaced by SU(1,1).
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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 [182]
Section IV (pp. 13–15) says that spacetimes with positive-definite induced metrics on T² fall into two classes: one with purely translational holonomies in M₀ and another in Mₛ. It explicitly says the tori in the M₀ class are spacelike in case (4.1), contrary to the claim that only the hyperbolic-hyperbolic sector permits spacelike T² slices. (LLM, conf=0.88)
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Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Lectures on Non-Perturbative Canonical Gravity
Ashtekar, A. (1991) · Advanced Series in Astrophysics and Cosmology · doi:10.1142/1321 · Cited by 872 · see citing works
Lorentz spacetimes of constant curvature
Mess, G. (2007) · Geometriae Dedicata · doi:10.1007/s10711-007-9155-7 · Cited by 278 · see citing works
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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
- Louko, J., & Marolf, D. M.
- Affiliations
- Syracuse University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1994-02-01
- Volume
- 11
- Issue
- 2
- Pages
- 311-330
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2051701084
- Cited by
- 35
- References
- 3
- FWCI
- 6.09
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Syracuse University
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- three-dimensional gravity, solution space, classical solutions, non-Hausdorff spaces, cotangent bundle, higher genus surfaces, quantization, momentum operator, spacetime metric
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