HOME

TheInfoList



Click Here for Items Related To - Kantowski–Sachs Metric
OR:
Kantowski–Sachs Metric on:   [Wikipedia]   [Google]   [Amazon]

In
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...
the Kantowski-Sachs metric (named after
Ronald Kantowski Ronald Kantowski (18 December 1939) is a theoretical cosmologist, well known in the field of general relativity as the author, together with Rainer K. Sachs, of the Kantowski–Sachs dust solutions to the Einstein field equation. These are a widel ...
and
Rainer K. Sachs Rainer Kurt "Ray" Sachs (born June 13, 1932) is a German-American mathematical physicist, with interests in general relativistic cosmology and astrophysics, as well as a computational radiation biologist. He is professor emeritus of Mathematics an ...
) describes a
homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
but
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's phys ...
universe whose spatial section has the topology of \mathbb \times S^. The metric is: : ds^ = -dt^ + e^ dz^ + \frac(d\theta^ + \sin^\theta d\phi^) The
isometry In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' mea ...
group of this spacetime is \mathbb \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 In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized famil ...
*
Dust solution In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has '' ...


Notes

General relativity Physical cosmology {{relativity-stub