Y Fujiwara et al 1993 Class. Quantum Grav. 10 859 doi:10.1088/0264-9381/10/5/006
Y Fujiwara, H Ishihara and H Kodama
Show affiliationsThe authors show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (i) no anisotropic expansion is allowed for Bianchi type V and VII (A not=0) and (ii) type IV and VI (A not=0,1) do not exist. In order to show them, they put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. They make clear the relation between the Bianchi-type symmetry of spacetime and spatial compactness, some parts of which seem to have gone unnoticed in the literature. Especially, it is shown under what conditions class-B Bianchi models do not possess compact spatial sections. Finally, they briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.
02.40.-k Geometry, differential geometry, and topology
04.20.Fy Canonical formalism, Lagrangians, and variational principles
04.20.Gz Spacetime topology, causal structure, spinor structure
Issue 5 (May 1993)
Y Fujiwara et al 1993 Class. Quantum Grav. 10 859
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