Three-dimensional classical spacetimes
Open accessAbstract
The authors extend what is known about the structure of (2+1)-dimensional gravitational field theories. The non-existence of any Newtonian limit to these theories is investigated in the presence of Brans-Dicke scalar fields and non-linear curvature terms in the gravitational action. A number of new exact static and non-static solutions of (2+1) general relativity with scalar field, perfect fluid and magnetic field sources are presented and studied in detail. Some of these possess a correspondence with (3+1) solutions of general relativity through a Kaluza-Klein type reduction and exhibit the 'wedge' structure of (3+1)-dimensional solutions describing line sources like vacuum strings. An algebraic classification of (2+1) gravitational fields is derived using the Bach-Weyl tensor. The description of the general cosmological solution is given in terms of arbitrary spatial functions independently specified on a spacelike surface of constant time together with a series approximation to spacetime in the vicinity of a general cosmological singularity.
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(2+1)-dimensional gravity does not have a good Newtonian limit.
“In particular, the theory does not have a good Newtonian limit [107, 49, 94].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [49]
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The (2 + 1)-dimensional black hole
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
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- Authors
- Barrow, J. D., Burd, A. B., & Lancaster, D.
- Affiliations
- University of Sussex (GB)
- ORCID
- Barrow, J D
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1986-07-01
- Volume
- 3
- Issue
- 4
- Pages
- 551-567
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2042454041
- Cited by
- 157
- References
- 5
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 4 · 2023: 4 · 2022: 5 · 2020: 7 · 2019: 5 · 2018: 4 · 2017: 27 · 2016: 4 · 2015: 2 · 2014: 1 · 2013: 3 · 2012: 3
- FWCI
- 3.56
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- three-dimensional gravity, Brans-Dicke scalar field, Newtonian limit, exact solutions, perfect fluid, magnetic field sources, Kaluza-Klein reduction, cosmological solutions, cosmological singularity, series approximation
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