Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-01-25
Class.Quant.Grav.10:859-868,1993
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages with one table, KUCP-55
Scientific paper
10.1088/0264-9381/10/5/006
We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to show them, we put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. We make clear the relation between the Bianchi type symmetry of space-time and spatial compactness, some part of which seem to be unnoticed in the literature. Especially, it is shown under what conditions class B Bianchi models do not possess compact spatial sections. Finally we briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.
Fujiwara Yasuhiro
Ishihara Hideki
Kodama Hideo
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