Chaos in the Gravitational Field| 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(17)-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].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 mar 2019