Kantowski-Sachs Models

In General [> s.a. spherical symmetry].
* Idea: Homogeneous cosmological models, in which the spatial isometry group acts multiply transitively.
* Line element: The usual form is

ds² = –dt² + A(t) dr² + B(t) d² .

* Remark: Used to describe the interior of a Schwarzschild black hole, for example re singularity resolution.
* Properties: Spatial topology S² × R, with possible discrete identifications; Spherically symmetric with an extra translation symmetry.

Special Cases > s.a. cosmological models [bounce].
* Conformally flat: Iff A(t) = B(t) cos t; tthen they admit progressing waves.
* Robinson-Bertotti: An electrovac solution of Einstein's equation, which is the direct product of a 2-sphere of radius (Q² + P²)^1/2 with a pseudosphere of the same radius; It has a six-parameter maximal symmetry group.
@ Robinson-Bertotti: Bertotti PR(59); Robinson BPAS(59); in Carter in(73); Silva-Ortigoza GRG(01), Sakalli GRG(03) [solution of Dirac equation]; Mazharimousavi & Halilsoy a0802 [generalized to Einstein-Yang-Mills-dilaton]; > s.a. particle models.

References > s.a. non-commutative field theory.
@ Perfect fluid: Kantowski & Sachs JMP(66) [dust]; Vajk & Eltgroth JMP(70); Collins JMP(77); Torrence & Couch GRG(88); Bombelli & Torrence CQG(90) [Ashtekar variables]; Dabrowski JMP(95) [dust].
@ Matter and radiation: Coley et al PRD(02)ap; Horváth & Kovács gq/06 [canonical theory].
@ Einstein-Yang-Mills: Donets et al PRD(99) [N = 2 susy].
@ Topology: Ellis GRG(71); Li & Hao PRD(03)ap [cannot be closed].
@ Related topics: Sanyal PLB(02) [with scalar, dynamical symmetries]; Shabbir gq/06 [Weyl collineations].

Quantum Theory > see minisuperspace quantum cosmology.

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