Chaos in the Gravitational Field  

In General
* Note: Unless otherwise specified, in this page gravitational theory is described by 4D general relativity.
* History: Study of the subject started with the mixmaster model, in the hope that it would lead to understanding anisotropy dissipation; The goal has not really been achieved, and has partly been taken over by inflation.
* Difficulty: One of the main indicators of chaos, the Lyapunov exponents, seems to be useless because of coordinate ambiguities; Must use topological indicators such as fractal basins of attraction, stochastic layers or cantori.
* Turbulence? Notice that, contrary to the situation in hydrodynamics, in general relativity there is no twist/vorticity for a congruence of geodesics.
@ General references: Frauendiener & Newman in(90); Ove GRG(90); Burd & Tavakol PRD(93); Núñez-Yépez et al pr(93); Szydłowski PLA(93), & Krawiec PRD(96); Rugh in(94), CSF(94); Biesiada CQG(95).
@ Invariant characterization: Biesiada & Rugh gq/94 [Maupertuis principle]; Cornish gq/96, gq/97-MG8, & Levin PRL(97)gq/96, PRD(97)gq/96; Witt & Schleich gq/96-proc; Szydłowski JMP(99) [and superspace metric]; Ramey & Balazs FP(01); Motter PRL(03)gq.

Classical Cosmological Models > s.a. cosmological models / collapse; chaos in bianchi models; string phenomenology.
@ FLRW spacetime: Calzetta & El Hasi CQG(93)gq/92; Calzetta in(94), & González PRD(95)gq/94 [and semiclassial general relativity]; Blanco et al GRG(94), GRG(95); Helmi & Vucetich PLA(97), Leach et al gq/01 [+ scalar, Painlevé]; Bombelli et al JMP(98)gq/97; Kamenshchik et al IJMPD(97)gq/98, IJMPD(98)gq [with cosmological constant], PRD(99)gq/98 [topological entropy]; Monerat et al PRD(98); Cotsakis & Miritzis gq/00-MG9; Pavluchenko & Toporensky G&C(00)gq/99; Toporensky gq/00-MG9; Motter & Letelier PRD(02)gq; Jorás & Stuchi PRD(03)gq [complexified a, bifurcations]; Tanaka et al CSF(05); Hrycyna & Szydłowski CSF(06)gq/05 [in terms of geodesics of Jacobi metric].
@ Inflation: Calzetta & El Hasi PRD(95)gq/94; Cornish & Levin PRD(96)ap/95; Cornish et al PRL(96)ap; Monerat et al gq/97-MG8; de Oliveira & Soares MPLA(98)gq; Easther & Maeda CQG(99)gq/97 [2-field]; de Oliveira et al PRD(99)gq [universality]; Easther & Parry PRD(00)hp/99 [inhomogeneous]; Jorás & Cárdenas PRD(03)gq/01 [and particle creation].
@ Einstein-Yang-Mills theory: Gal'tsov & Volkov PLB(91) [absent in isotropic case]; Darian & Künzle CQG(95) [axisymmetric]; Barrow & Levin PRL(98)gq/97; Matinyan gq/00-MG9.
@ Inhomogeneous models: Weaver et al PRL(98)gq/97; Benini & Montani gq/07-MGXI [covariant description], gq/07-MGXI [quantum aspects].
@ Related topics: Kandrup & Drury ANYAS(98)ap [classification of Hamiltonians]; Heinzle et al PRD(05)gq/04, PRD(06)gq [Bianchi IX and Kantowski-Sachs + fluid, questioning]; Li et al CQG(05)ap [barotropic fluid and quintessence, alleviate fine tuning].

Other Theories and Systems > s.a. brane cosmology.
* Higher dimensions: The generically chaotic BKL behavior near a spacelike singularity disappears in dimension D = d + 1 > 10.
@ String theory: Barrow & Dąbrowski PRD(98)ht/97 [no chaos]; Damour & Henneaux PRL(00)ht [Einstein-dilaton-p-form, oscillations], PRL(01)ht/00 [as chaotic quantum billiard]; Forte CQG(09)-a0812 [formalism for billiard representation].
@ Higher dimensions: Elskens & Henneaux CQG(87), Helmi & Vucetich PLA(95) [Kaluza-Klein]; Damour et al PLB(01)ht [hyperbolicity of Kac-Moody algebras].
@ Quantum gravity: Dittrich et al PLB-a1602 [and continuity of observables]; > s.a. minisuperspace quantum cosmology [semiclassical and quantum chaos].

Consequences and Related Topics > s.a. chaos; phenomenology of geometry in quantum gravity.
@ Patterns in cosmology: Barrow & Levin ap/99-proc; Levin & Barrow CQG(00)gq/99.
@ Other: Hu et al gq/93-proc [dissipative processes]; Lombardo et al MPLA(99) [particle creation]; Haggard PRD(13)-a1211 [and quantum gravity, from quantized volumes].


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