Isotropic singularities and the polytropic equation of state
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Following a previous letter (Tod 1989), an initial-value problem for perfect-fluid cosmologies with polytropic equation of state is presented where the data are the 3-metric of an initial isotropic singularity.
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The metric tensor in isotropic singularities can be obtained by conformal rescaling from a regular metric, and its Weyl tensor equals that of a regular metric, hence remains finite.
“The metric tensor in this case can be obtained by a conformal rescaling from a regular ( i.e. non-singular) metric tensor, and presents nice behavior from conformal geometric viewpoint. Because the Weyl tensor C abc d is invariant at conformal rescaling, the main feature of the isotropic singularities is that the Weyl tensor equals that of a regular metric, hence remaining finite.”
From On the Weyl curvature hypothesis (2013) · cites this paper as [7]
The opening passage (p. L79) describes the physical spacetime as conformally related to an unphysical spacetime in which the singularity is a smooth surface. The discussion on p. L82 treats the Weyl tensor as having an initial value, but our copy does not state that the physical Weyl tensor equals the regular metric’s Weyl tensor under rescaling or explicitly conclude that it remains finite. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIsotropic singularities automatically satisfy a version of the Weyl curvature hypothesis stating that the Weyl curvature remains finite at the singularity.
“An important class of singularities which automatically satisfy a version of the WCH (stating that the Weyl curvature remains finite at singularity) are the isotropic singularities .”
From On the Weyl curvature hypothesis (2013) · cites this paper as [7]
The opening discussion describes an isotropic singularity as a smooth surface in a conformally related, unphysical spacetime. The closing discussion (p. L82) speaks of the Weyl tensor at that initial surface, but the paper does not explicitly state that the physical Weyl curvature remains finite there or formulate the stated version of the Weyl curvature hypothesis. (LLM, conf=0.76)
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Cites
Isotropic singularities and the γ=2 equation of state
Tod, K. P. (1990) · Classical and Quantum Gravity · doi:10.1088/0264-9381/7/1/004 · Cited by 33 · see citing works
Self-citationVorticity and isotropic singularities
Goode, S. W. (1987) · General Relativity and Gravitation · doi:10.1007/bf00759143 · Cited by 13 · see citing works
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Isotropic Cosmological Singularities: I. Polytropic Perfect Fluid Spacetimes
Anguige, K., & Tod, K. P. (1999) · Annals of Physics · doi:10.1006/aphy.1999.5946 · Cited by 72 · see citing works
Self-citationIsotropic cosmological singularities: other matter models
Tod, K. P. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/3/309 · Cited by 51 · see citing works
Self-citationOn the Weyl curvature hypothesis
Stoica, O. C. (2013) · Annals of Physics · doi:10.1016/j.aop.2013.08.002 · Cited by 22 · see citing works
Nesteruk, A. V. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/1/004 · Cited by 10 · see citing works
- Authors
- Tod, K. P.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Tod, K P
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1991-04-01
- Volume
- 8
- Issue
- 4
- Pages
- L77-L82
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2009261063
- Semantic Scholar
- 5b2d637bbbe715506d553fea8ab6f43630f37d91
- Cited by
- 27
- References
- 2
- Citations by year
- 2024: 3 · 2021: 2 · 2018: 2 · 2017: 1 · 2016: 1 · 2014: 2 · 2013: 3
- FWCI
- 3.57
- 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 › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- isotropic singularity, polytropic equation of state, perfect fluid cosmology, initial value problems, cosmological singularity, initial data
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