4 Midisuperspaces: Classical Aspects

A rough classification of the symmetry reductions of general relativity can be made by considering the dimension of the isometry group of the metric. In many cases this is equivalent to classifying the spacetime metrics for the midisuperspace model in question according to the number of Killing vector fields that they have. Though this is a sensible approach, especially when the Killing fields commute, this is not always the most natural way to describe all the interesting symmetry reductions, in particular, when spherical symmetry is present.

 4.1 One-Killing vector reductions
 4.2 Two-Killing vector reductions
 4.3 Spherical symmetry

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