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Cited by 411Relativity and Gravitational TheoryCosmology and Gravitation TheoriesAdvanced Differential Geometry Research

Dynamics of Pressure-Free Matter in General Relativity

Ellis, G. F. R·1967·Journal of Mathematical Physics
DOI 10.1063/1.1705331
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Abstract

An orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust-filled space-time. This is used to study dust-filled spaces in which there exist multiply transitive groups of motions; all such spaces are classified in detail. Spaces containing shear-free dust are also considered; it is shown that σ = 0 ⇒ ωΘ = 0. Three classes of solution with σ = 0, ω ≠ 0 are studied. Several new solutions of the field equations are contained in these results.

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Crossref · 10.1063/1.1705331

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22 of 22 references verified0 citation errors · 0 not checkable

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  • Instead of quantizing the infinitesimal constraint, one can solve the diffeomorphism constraint by group averaging using the known action of diffeomorphisms on the auxiliary manifold.

    “Instead of quantizing the infinitesimal constraint we can use the known action of diffeomorphisms on the auxiliary manifold to solve the constraint by group averaging [33].”

    From Loop quantum cosmology: I. Kinematics (2000) · cites this paper as [33]

  • Graph symmetries must be taken into account in group averaging.

    “But graph symmetries have to be taken properly into account [33,34], which will be done now for the example of Bianchi IX.”

    From Loop quantum cosmology: I. Kinematics (2000) · cites this paper as [33]

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Authors
Ellis, G. F. R.
Affiliations
The University of Texas at Austin (US)
Corresponding author
Ellis, G. F. R
ORCID
Ellis, G. F. R
Venue
Journal of Mathematical Physics
Publisher
AIP Publishing
Published
1967-05-01
Volume
8
Issue
5
Pages
1171-1194
ISSN
  • 0022-2488 (ISSN-L)
  • 1089-7658
DOI
10.1063/1.1705331
OpenAlex
W2129200752
Cited by
411
References
22
Citations by year
2026: 6 · 2025: 6 · 2024: 9 · 2023: 7 · 2022: 11 · 2021: 13 · 2020: 9 · 2019: 7 · 2018: 8 · 2017: 12 · 2016: 5 · 2015: 12 · 2014: 12 · 2013: 8 · 2012: 7
FWCI
5.42
Type
journal article
Language
en
Open access
closed
Locations
Journal of Mathematical Physics (publishedVersion)
Funders
University of Cambridge
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
orthonormal tetrad, exact solutions of Einstein field equations

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