(2+1) gravity for higher genus in the polygon model
Open accessAbstract
We construct explicitly a (12g-12)-dimensional space P of unconstrained and independent initial data for 't Hooft's polygon model of (2+1) gravity for vacuum spacetimes with compact genus-g spacelike slices, for any g >= 2. Our method relies on interpreting the boost parameters of the gluing data between flat Minkowskian patches as the lengths of certain geodesic curves of an associated smooth Riemann surface of the same genus. The appearance of an initial big-bang or a final big-crunch singularity (but never both) is verified for all configurations. Points in P correspond to spacetimes which admit a one-polygon tessellation, and we conjecture that P is already the complete physical phase space of the polygon model. Our results open the way for numerical investigations of pure (2+1) gravity.
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't Hooft's approach has been used mainly to understand point particle dynamics, but recent progress has allowed a general description of topologically nontrivial compact spaces.
“This approach has been used mainly to understand point particle dynamics, but recent progress has allowed a general description of topologically nontrivial compact spaces [169].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [169]
The Introduction (pp. 1–2) says the paper develops explicit initial data for compact higher-genus spaces, supporting the claim of progress beyond particle dynamics. But it does not establish that the approach had been used mainly for point particles, and it conjectures—rather than proves—that its higher-genus solution space is complete. The Discussion (§5) also says including particles remains a next step for this work. (LLM, conf=0.84)
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Research works printed but not linked: 16
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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
Dittrich, B., & Höhn, P. A. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/11/115009 · Cited by 69 · see citing works
- Authors
- Kádár, Z., & Loll, R.
- Affiliations
- Utrecht University (NL)
- Perimeter Institute (CA)
- ORCID
- Loll, R
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2004-04-14
- Volume
- 21
- Issue
- 9
- Pages
- 2465-2491
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2054626444
- Cited by
- 6
- References
- 0
- Citations by year
- 2012: 1
- FWCI
- 0.63
- 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)
- Utrecht University Repository (Utrecht University) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- three-dimensional gravity, polygonal models, higher genus, initial data, Riemann surfaces, geodesics, initial singularity, big crunch singularity, phase space, vacuum spacetimes
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