Friedmann limits of rotating hypersurface-homogeneous dust models
arXiv:gr-qc/0102040 · doi:10.1063/1.1378304
Abstract
The existence of Friedmann limits is systematically investigated for all the hypersurface-homogeneous rotating dust models, presented in previous papers by this author. Limiting transitions that involve a change of the Bianchi type are included. Except for stationary models that obviously do not allow it, the Friedmann limit expected for a given Bianchi type exists in all cases. Each of the 3 Friedmann models has parents in the rotating class; the k = +1 model has just one parent class, the other two each have several parent classes. The type IX class is the one investigated in 1951 by Goedel. For each model, the consecutive limits of zero rotation, zero tilt, zero shear and spatial isotropy are explicitly calculated.
39 pages, LaTeX, 1 postscript figure. Subjects: General relativity, exact solutions, cosmology
References in corpus (4)
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- Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 2: One Killing field spanned on u^α and w^α
- Rotating Bianchi type V dust models generalizing the k = -1 Friedmann model