The evolution of gravitating point particles in 2+1 dimensions
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The complete history of a set of classical gravitating point particles in 2+1 dimensions is considered, in the absence of a cosmological constant. The author formulates the equations of motion in terms of a time-dependent tessellation of Cauchy surfaces, of which a number of examples were run on a computer. In particular he focuses on the initial and final states. A given universe may either continue to expand for ever or shrink to a point in a final crunch, the latter being the rule rather than an exception. The past history may either be a 'big bang' or an infinitely large shrinking universe. Universes with g=0 may have both a bang in the past and a crunch in the future. Universes with g<or=1 and neither a bang in the past nor a crunch in the future were not found. His findings must have important consequences for any possible quantized version of such a system.
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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 [253]
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
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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
- Hooft, G. '.
- Corresponding author
- Hooft, G 't
- ORCID
- Hooft, G 't
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1993-05-01
- Volume
- 10
- Issue
- 5
- Pages
- 1023-1038
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2166489988
- Cited by
- 74
- References
- 1
- Citations by year
- 2026: 1 · 2022: 4 · 2021: 3 · 2020: 2 · 2019: 1 · 2018: 1 · 2017: 2 · 2016: 2 · 2015: 6 · 2014: 2 · 2013: 1 · 2012: 2
- FWCI
- 7.67
- Type
- journal article
- Language
- en
- Open access
- Licence
- other-oa
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- three-dimensional gravity, classical gravity, equations of motion, Big Bang, initial and final states, cosmological evolution
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