Global structure of the ''Kantowski--Sachs'' cosmological models

Journal Article · Tue Nov 01 04:00:00 EST 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523191· OSTI ID:7213838

Collins, C B

A discussion is given of the ''Kantowski--Sachs'' cosmological models; these are defined locally as admitting a four-parameter continuous isometry group which acts on spacelike hypersurfaces, and which possesses a three-parameter subgroup whose orbits are 2-surfaces of constant curvature (i.e., the models possess spherical symmetry, combined with a translational symmetry, and can thus be regarded as nonempty analogs of part of the extended Schwarzschild manifold). It is shown that all general relativistic models in which the matter content is a perfect fluid satisfying reasonable energy conditions are geodesically incomplete, both to the past and to the future, and that at each resulting singularity the fluid energy density is infinite. In the case where the fluid obeys a barotropic equation of state (which includes all known exact perfect fluid solutions) the field equations are shown to decouple to form a plane autonomous subsystem. This subsystem is examined using qualitative (Poincare--Bendixson) theory, and phase--plane diagrams are drawn depicting the behavior of the fluid's energy density and shear anisotropy in the course of the models' evolution. Further diagrams depict the conformal structure of these universes, and a table summarizes the asymptotic properties of all physically relevant variables.

• Research Organization: Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
• OSTI ID: 7213838
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 18:11; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COSMOLOGICAL MODELS
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF STATE
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
LIE GROUPS
MATHEMATICAL MODELS
SYMMETRY GROUPS