# Kantowski-Sachs metric

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.