Astronomy:Kantowski–Sachs metric

Short description: Metric of a homogenous universe

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 $\mathbb{ℝ}\times S^2$. The metric is:

$d{s}^2=-d{t}^2+e^{2\sqrt{\mathrm{\Lambda }}t}d{z}^2+\frac{1}{\mathrm{\Lambda }}(d{\theta }^2+{\sin }^2\theta d{\varphi }^2)$

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.

See also

• Bianchi classification
• Dust solution