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:

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

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article relies largely or entirely on a single source. (January 2020) This article relies too much on references to primary sources. (January 2020)

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

Notes

This relativity-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e