Gödel Solution

In General > s.a. [relativistic cosmological models]; causality; particle models; quantum field theory in curved spacetime.
* Idea: A rotating cosmological solution with pressure-free perfect fluid matter on an R⁴ manifold, which shattered some preconceived ideas, since the local definition of inertial frame disagrees with the global one; It violates causality and is not time-orientable.
* Remark: A generalized form, actually described originally by Gödel, is a family of metrics with isometry group SO(2,1) × SO(2) × R.
* Properties: It has a 5-parameter group of isometries which acts transitively, and there are closed timelike curves through all points; Any two points can be joined by a timelike curve; There are no non-empty achronal sets.
* Metric: Constructed from Maurer-Cartan forms of a suitable Lie group,

ds² = –dt² + dx² – exp{2 x} dy² + dz² – 2 exp{ x} dt dy (partial) ,

with fluid 4-velocity u = /t; = const = magnitude of vorticity of u^a, 4 = ².

References
@ General: Gödel RMP(49) + GRG(00), in(52) + GRG(00); Kundt ZP(56); in Hawking & Ellis 73, 168–170; Bonnor et al CQG(98)gq/97 [exterior]; Nemeti et al a0811 [visualization]; Rindler in(09) + AJP(09)jun.
@ Energy and momentum: Dabrowski & Garecki CQG(02)gq/01, PRD(04)gq/03; Sharif IJMPA(03).
@ Light cones, causality: Pfarr GRG(81); Malament JMP(87); Ozsváth & Schucking AJP(03)aug; Dautcourt & Abdel-Megied CQG(06)gq/05; Gleiser et al CQG(06)gq/05 [closed timelike curves]; Rosa & Letelier GRG(07)gq [stability of closed timelike curves].
@ Related topics: Saha & Chowdhury PS(00) [geodesic deviation]; Barrow & Tsagas CQG(04)gq/03 [stability]; Aydogdu & Salti gq/05-wd [spin-1 particle creation]; Sahdev et al gq/06 ['travel guide' and sketches]; Marecki gq/07 [wave equation]; > s.a. diffusion.

Similar Solutions and Other Theories > s.a. black holes in modified theories [5D Schwarzschild-Gödel]; branes.
@ 2+1: Harriott & Williams GRG(01) [pfluid, with kink]; Sousa et al a0705 [classification and properties]; Gürses a0812.
@ 5D: Rebouças & Teixeira JMP(98); Behrndt & Pössel PLB(04)ht/03 [supergravity, < 0].
@ Variations: Romano & Goebel GRG(03) [with electromagnetic field]; Dryuma gq/05 [Riemann extension]; > s.a. kerr-newman spacetime.
@ Chern-Simons-modified gravity: Konno et al PRD(08); Furtado et al PRD(09)-a0906; > s.a. higher-order theories.
@ Other theories: Åman et al CQG(98)gq/97, Fonseca-Neto & Rebouças GRG(98)gq [Riemann-Cartan]; Barrow & Dabrowski PRD(98) [low-energy string theory]; Ozsváth & Schücking CQG(01) [newtonian analog]; Caldarelli & Klemm CQG(04)ht/03 [4D, supersymmetric]; Gürses et al CQG(05)ht/03, & Sarioglu CQG(05)ht [various dimensions]; Obukhov & Vargas PLA(04)gq [teleparallel gravity]; Gürses GRG(09)-a0801 [Einstein-Aether theory]; Rebouças & Santos PRD(09)-a0906 [in f(R) gravity].

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