Kantowski-Sachs Spacetimes

In General > s.a. spherical symmetry in general relativity.
* 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) dΩ² .

* Remark: Used to describe the interior of a Schwarzschild black hole, for example re singularity resolution.
* Properties: Spatial topology S² × \(\mathbb R\), with possible discrete identifications; Spherically symmetric with an extra translation symmetry.
@ Geometry: Shabbir & Mehmood MPLA(07)gq/06 [Weyl collineations]; Heinzle PRD(11)-a1105 [constant-mean-curvature slicings]; Shabbir & Iqbal a1110 [proper homothetic vector fields]; Shabbir et al a1308 [proper conformal vector fields].
@ Topology: Ellis GRG(71); Li & Hao PRD(03)ap [cannot be closed].

Special Cases > s.a. cosmological models [bounce].
* Conformally flat: A Kantowski-Sachs spacetime is conformally flat iff A(t) = B(t) cos t; Then, and only then, it admits progressing waves.
* Robinson-Bertotti solution: 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 solution: Bertotti PR(59); Robinson BAPS(59); in Carter in(73); Silva-Ortigoza GRG(01), Sakalli GRG(03) [solution of Dirac equation]; Mazharimousavi et al GRG(10)-a0802 [generalized to Einstein-Yang-Mills-dilaton]; Garfinkle & Glass CQG(11)-a1109 [and Melvin spacetimes]; Ottewill & Taylor PRD(12)-a1209 [quantum theory of a massless scalar field]; Halilsoy & Mazharimousavi PRD(13)-a1211 [and Melvin spacetimes]; Clément CQG(14)-a1311 [in 5D quadratic gravity]; > s.a. lovelock gravity; particle models.

Other References > s.a. non-commutative field theory.
@ With a 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]; Adhav et al IJTP(08) [+ massless scalar].
@ With matter and radiation: Coley et al PRD(02)ap; Horváth & Kovács PADEU-gq/06-proc [canonical theory].
@ With a scalar field: Sanyal PLB(02) [dynamical symmetries]; Reddy et al IJTP(09).
@ Einstein-Yang-Mills theory: Donets et al PRD(99) [N = 2 supersymmetry].
@ Perturbations: Keresztes et al proc(14)-a1304, Bradley et al a1303-MG13, Keresztes et al JCAP(15)-a1507 [with a cosmological constant].
@ In f(R) gravity: Shamir ASS(10)-a1006; Leon & Saridakis CQG(11)-a1007 [f(R) = Rⁿ gravity]; Leon & Roque JCAP(14)-a1308.
@ In f(T) gravity: Rodrigues et al ASS(15)-a1408 [and Bianchi I & III]; Amir & Yussouf IJTP(15)-a1502.
@ In other theories: Obregón & Preciado AIP(11)-a1305 [Hořava-Lifshitz gravity]; > s.a. einstein-æther theories; non-commutative cosmology.

Quantum Theory > s.a. minisuperspace quantum cosmology; GUP phenomenology.
@ General references: Louko & Vachaspati PLB(89); Chakraborty MPLA(91), & Chakravarty IJMPA(98); Uglum PRD(92); Mazzitelli PRD(92) [and spherical symmetry]; Conradi CQG(95)gq/94; Simeone GRG(00)gq/01, GRG(02)gq; Shen & Zhang IJTP(00) [from sqrt of Wheeler-DeWitt equation]; Cordero et al PRD(11)-a1102 [deformation quantization]; Joe & Singh CQG(15)-a1407 [in lqc]; Alvarenga et al a1506 [fluid, two approaches to time]; Pal & Banerjee CQG*(15)-a1506 [unitary evolution].
@ Lqg approach: Modesto IJTP(06)gq/04 [lqg/Bohr compactification], CQG(06)gq/05 [and black hole singularity]; Chiou PRD(08) [with lqc corrections].

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