Kantowski–Sachs metric

In general relativity the Kantowski-Sachs metric (named after Ronald Kantowski and Rainer K. Sachs)^[1] describes a homogeneous but anisotropic universe whose spatial section has the topology of ${\displaystyle \mathbb {R} \times S^{2}}$. The metric is:

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

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

See also

• Bianchi classification
• Dust solution