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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