Kantowski-Sachs metric

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In general relativity the Kantowski-Sachs metric describes a homogeneous but anisotropic universe whose spatial section has the topology of  \mathbb{R} \times S^{2}. The metric is:

ds^{2} = -dt^{2} + e^{2\sqrt{\Lambda}t} dz^{2} + \frac{1}{\Lambda}(d\theta^{2} + \sin^{2}\theta d\phi^{2})

The isometry group of this spacetime is  \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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