A new derivation of the Robertson-Walker metrics is presented which elucidates the relationship between these spatially homogeneous and isotropic models and certain spatially homogeneous but anisotropic models (``three-cylinder universes''). The evolutionary equations for Robertson-Walker models containing as many as four distinct noninteracting relativistic fluids (each obeying a gamma-law equation of state) are examined, and 25 exact closed-form solutions of this type are presented explicitly.
We review spatially homogeneous, axially symmetric universes containing either an ideal fluid (with a γ-law equation of state) or a uniform magnetic field parallel to the symmetry axis or both. In many cases, the field equations may be solved by the technique (described in detail) of replacing the cosmic time by a suitably chosen timelike parameter. We systematically derive all known exact solutions for such universes.
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