Kantowski-Sachs metric

In general relativity the Kantowski-Sachs metric (named after Ronald Kantowski and Rainer K. Sachs) describes a homogeneous but anisotropic universe whose spatial section has the topology of ${\displaystyle \mathbb {R} \times S^{2}}$. The metric is:

The isometry group of this spacetime is ${\displaystyle \mathbb {R} \times SO(3)}$. Remarkably, the isometry group does not act simply transitively on spacetime, nor does it possess a subgroup with simple transitive action.

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