Topology and classical geometry in (2 + 1) gravity
Open accessAbstract
The structure of the spacetime geometry in (2 + 1) gravity is described by means of a foliation in which the space-like surfaces admit a tessellation made of polygons. The dynamics of the system is determined by a set of 't Hooft's rules which specify the time evolution of the tessellation. We illustrate how the non-trivial topology of the universe can be described by means of 't Hooft's formalism. The classical geometry of a universe with the spatial topology of a torus is considered and the relation between 't Hooft's transitions and modular transformations is discussed. The universal covering of spacetime is constructed. The non-trivial topology of an expanding universe gives origin to a redshift effect; we compute the value of the corresponding `Hubble's constant'. Simple examples of tessellations for universes with the spatial topology of a surface with higher genus are presented.
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The first discrete formulation designed explicitly for 2+1 dimensions was developed by 't Hooft et al.
“The first discrete formulation designed explicitly for 2 + 1 dimensions was developed by’ t Hooft et al. [250, 252, 253, 124, 274, 156].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [124]
The Introduction identifies ’t Hooft’s formalism as a formulation of (2+1)-dimensional gravity, and §2 describes its polygon tessellation, supporting the attribution of a discrete formulation to him. The paper does not establish that it was the first such formulation. (LLM, conf=0.85)
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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
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Research works printed but not linked: 1
- Arnowitt R, Deser S and Misner C W 1962 Gravitation; an Introduction to Current Research ed L Witten (New York: Wiley)
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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
- Franzosi, R., & Guadagnini, E.
- Affiliations
- University of Pisa (IT)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1996-03-01
- Volume
- 13
- Issue
- 3
- Pages
- 433-460
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1975127138
- Cited by
- 14
- References
- 1
- Citations by year
- 2016: 1
- FWCI
- 1.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion)
- Use Siena air (University of Siena) (submittedVersion)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- three-dimensional gravity, spacetime topology, foliations, toroidal topology, modular transformations, universal cover, red shift, Hubble constant, higher genus surfaces, classical geometry
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