Chaos
in the Gravitational Field| Chaos
in the Gravitational Field |
In General
* History: Study 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); Szydlowski 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-in, & Levin
PRL(97)gq/96,
PRD(97)gq/96;
Witt & Schleich gq/96-in;
Szylowski 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.
@ FRW: 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-in;
Pavluchenko & Toporensky
G&C(00)gq/99;
Toporensky gq/00-in;
Motter & Letelier
PRD(02)gq;
Jorás & Stuchi PRD(03)gq [complexified a,
bifurcations]; Tanaka et al CSF(05);
Hrycyna & Szydlowski CSF(06)gq/05 [ito
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-in;
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: Gal'tsov & Volkov PLB(91)
[absent in isotropic case]; Darian & Künzle CQG(95)
[axisymmetric]; Barrow & Levin
PRL(98)gq/97;
Matinyan gq/00-in.
@ Inhomogeneous: Weaver et al PRL(98)gq/97;
Benini
& Montani gq/07-in
[covariant description], gq/07-in
[quantum aspects].
@ Related topics: Kandrup & Drury ap/98 [classification
of Hamiltonians]; Heinzle et al PRD(05)gq/04,
PRD(06)gq [Bianchi
IX and KS + fluid, questioning];
Li et al CQG(05)ap
[barotropic
fluid and quintessence, alleviate fine-tuning].
Other Theories and Systems > s.a. brane
cosmology; minisuperspace quantum
cosmology [semiclassical
and quantum chaos].
* Higher dimensions:
The generically chaotic BKL behavior near a spacelike singularity disappears
in dim D = d +
1 > 10.
@ String theory: Barrow & Dabrowski PRD(98)ht/97 [no
chaos]; Damour & Henneaux PRL(00)ht [Einstein-dilaton-p-form,
oscillations], PRL(01)ht/00 [as
chaotic quantum billiard].
@ Higher dimensions: Elskens & Henneaux CQG(87),
Helmi & Vucetich PLA(95)
[Kaluza-Klein]; Damour et al PLB(01)ht [hyperbolicity
of Kac-Moody algebras].
Consequences > s.a. chaos.
@ Patterns in cosmology: Barrow & Levin ap/99-in;
Levin & Barrow
CQG(00)gq/99.
@ Other: Hu et al gq/93-in
[dissipative processes]; Lombardo
et al MPLA(99)
[particle creation].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
20 jun 2008