Astronomy: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 [math]\displaystyle{ \mathbb{R} \times S^{2} }[/math]. The metric is:

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

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

See also

• Bianchi classification
• Dust solution