Types of Spacetimes  

General Types > s.a. causality conditions; causality-violating; Geodesically Complete; lorentzian geometry.
* Generic: Every timelike or null geodesic contains at least one point with nonzero Ka Kb K[c Rd]ab[e Kf ] (effective curvature).
* Strongly asymptotically predictable: Essentially, a spacetime with no naked singularities, except white holes; An asymptotically flat spacetime (M, g), with compactification (M', g'), such that in M there is a sufficiently large open region V (i.e., which contains the past of +, the closure of M' J(+) is in V), which makes (V', g') globally hyperbolic.
* Totally vicious: A spacetime (M, g) such that for all p in M, I(p) I +(p) = M, i.e., the Lorentzian distance function d(p, q) = ; Examples are a 2-torus with the usual metric, the Gödel spacetime, the Kerr-Newman solution with a2 + e2 > m2.
@ Generic: Beem & Harris GRG(93).
@ Totally vicious: Ikawa & Nakagawa JoG(88); Matori JMP(88); Kim & Kim JMP(93).
@ Related topics: Markowitz GRG(82) [conformally hyperbolic]; Hall CQG(96) [decompositions into constant-type regions]; Ramos et al JMP(03) [double warped, invariant characterization]; Pina & Tenenblat JGP(07) [conformally flat].
> Ito curvature: see petrov types; riemann tensor [constant invariants]; Silent Universe; solutions of general relativity; weyl tensor [purely magnetic].
> Ito physical interpretation: see asymptotically flat; black holes; cosmological models; Non-Imprisonment.
> Topologically non-trivial: see geon; wormhole.

Cylindrically Symmetric > s.a. axisymmetry; models in canonical general relativity; [cosmic strings].
* Idea: Axisymmetry with an additional z-invariance.
@ Levi-Civita: Rao JPA(71) [radiating]; Delice APPB(06)gq/04 [vacuum, non-static], gq/05-wd [radiating].
@ Other general relativity: Carot et al CQG(99)gq [def]; Arazi & Simeone GRG(00)gq; Barnes CQG(00)gq = gq/00-in; Senovilla & Vera CQG(00)gq [dust cosmology]; Klepac & Horsky CQG(00)gq [Einstein-Maxwell + fuid]; Qadir et al CQG(00)gq/07 [homotheties]; Fjällborg CQG(07) [static, Einstein-Vlasov]; Zofka & Bicak CQG(08)-a0712 [static, with cosmological constant].

Einstein Manifold / Metric / Space / Static Universe > s.a. embeddings; de Sitter.
$ Def: A manifold with Lorentzian metric such that Rab = c gab, with c a constant.
* Brinkman's theorem: Two Einstein spaces can be conformally mapped to each other only if both are Ricci-flat pp-waves, or both are conformally flat [@ Daftardar-Gejji GRG(98), with matter].
@ General references: Petrov 69; Besse 87; Gao JDG(90); Dancer & Strachan CQG(02)m.DG [on TSn+1]; Barrow et al CQG(03) [with pfluid, stability]; Gibbons et al CQG(04)ht [5D, on S3-bundle over S2]; Böhm JDG(04) [and simplicial complexes]; Boyer et al AM(05) [on spheres]; Mitra a0806-PRD.
@ Conformally Einstein: Gover m.DG/04-in [almost]; Gover & Nurowski JGP(06) [obstructions, n-dimensional].

Stationary and Related Spacetimes > s.a. general relativity solutions with symmetries; Papapetrou Theorem.
* Ehlers group: A symmetry group of the vacuum Einstein equation for strictly stationary spacetimes.
* Pseudostationary: A spacetime with a one-parameter isometry group, such that its orbits are timelike curves at sufficiently large asymptotic distances (if they were timelike everywhere, the spacetime would be stationary).
@ Static: Bartnik & Tod CQG(06)gq/05 [and spatial 3-metrics]; Sánchez & Senovilla CQG(07) [global orthogonal decomposition]; > s.a. anti-de sitter, Ultrastatic.
@ Related topics: Mars CQG(01)gq [Ehlers group]; > s.a. spin coefficients.

Other Symmetries s.a. general relativity solutions with symmetries.
@ Flat: Charette et al JGP(03) [3D, with closed timelike curves]; Barbot JGP(04)m.GT [globally hyperbolic]; Guediri DG&A(04) [compact]; Adler & Overduin GRG(05) [approximately flat]; Bonsante JDG(05) [with compact hyperbolic Cauchy surfaces]; > s.a. conservation laws, minkowski.
@ Plane symmetric: Feroze et al JMP(01) [classification].
@ Homogeneous: Valiente CQG(98)gq, CQG(99)gq/98, CQG(00) [polyhomogeneous]; Meessen LMP(06) [with canonically homogeneous null geodesics]; > s.a. bianchi models and FRW models.
> Other spatial symmetries: see Self-Similar; spherical.

Other Specific Forms > s.a. coordinates [forms of line element]; Newman-Tamburino; W-Universe; Misner Metric; Misner Space.
* Generalized Lewis-Papapetrou: A metric of the form ds2 = –f (dt + i dxi)2 + f –1 gij dxi dx j ; > s.a. teleparallel.
* Painlevé-Gullstrand: A metric written in the form ds2 = –[c2(r, t) – f 2(r, t)] dt2 – 2 f(r, t) dr dt + r2 d2.
@ Painlevé-Gullstrand: in Visser IJMPD(03)ht/01; Fischer & Visser AP(03)cm/02 [effective geometry]; Natario a0805 [for Kerr]; > s.a. schwarzschild.
@ Other types: Clarke & Joshi CQG(88) [reflecting]; > types of metrics [including singular, distributional].


Main pageAbbreviationsJournalsCommentsOther sitesAcknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 15 jul 2008