Chaotic Motion in a Gravitational Field  

Geodesic Motion of Test Bodies > s.a. dynamics of gravitating bodies; lyapunov exponents.
* Note: Unless otherwise specified, in this page gravitational theory is described by 4D general relativity.
@ Perturbed Schwarzschild: Bombelli & Calzetta CQG(92); Moeckel CMP(92); Bombelli in(94); Cornish & Frankel PRD(97)gq/96; Vieira & Letelier PRL(96); Letelier & Vieira CQG(97)gq, PRD(97)gq; de Moura & Letelier PRE(00)cd/99 [Schwarzschild with halo].
@ Two centers: Contopoulos PRS(90), PRS(91); Dettmann et al PRD(94), Frac(95)gq; Yurtsever PRD(95)gq/94; Cornish & Gibbons CQG(97)gq/96 [Einstein-Maxwell-dilaton]; Contopoulos & Harsoula JMP(04) [two fixed black holes].
@ Static axisymmetric: Karas & Vokrouhlický GRG(92) [Ernst spacetime]; Sota et al CQG(96)gq/95 [vacuum], gq/96 [non-vacuum], comment Vieira & Letelier CQG(96)gq.
@ Other isolated bodies: Letelier & Motter PRE(99)ap/02 [monopole + quadrupole]; Guéron & Letelier PRE(01)ap, ap/01 [axisymmetric + quadrupole]; Chen & Wang CQG(03)gq/02 [charged black hole + dipoles]; Dubeibe et al PRD(07); Han PRD(08)-a1006 [rotating neutron star]; Dalui et al a1803 [near an event horizon]; De Falco a2001 [Kerr equatorial orbits]; Xue a2012, a2012 [perturbed Schwarzschild and Kerr, KAM theory].
@ In FLRW spacetime: Lockhart et al PRD(82); Tomaschitz JMP(91).
@ Other cosmological models: Kandrup NYAS(98)ap/99 [time-varying background].
@ Cosmic strings: Frolov & Larsen CQG(99)gq [scattering by black holes].
@ In gravitational waves: Podolský & Veselý PRD(98)gq, CQG(98)gq, CQG(99)gq [pp-waves]; Veselý & Podolský PLA(00)gq; Podolský & Kofroň CQG(07)-a0705, Sakalli & Halilsoy ChPL(11)-a0706 [Kundt spacetimes].

Motion of Other Bodies > s.a. black-hole phenomenology; Hill System; sources of gravitational waves.
* Coalescing binaries: While there are chaotic regions of phase space without radiation reaction, in practice with radiation chaos has no effect within inspiral timescales.
@ Spinning particle in Schwarzschild spacetime: Suzuki & Maeda PRD(97)gq/96, PRD(00)gq/99; Kao & Cho PLA(05)gq/04; Koyama et al PRD(07); Verhaaren & Hirschmann PRD(10)-a0912, comment Lukes-Gerakopoulos a1604.
@ Spinning particle in Kerr spacetime: Suzuki & Maeda PRD(98)gq/97; Hartl PRD(03)gq/02, PRD(03); Han GRG(08)-a1006 [numerical]; > s.a. kerr spacetime.
@ Charged particle around black hole: Aguirregabiria PLA(97) [four extreme Reissner-Nordström black holes]; Takahashi & Koyama ApJ(09)-a0807; Kopáček et al AIP(10)-a1011 [charged particle around Kerr spacetime with magnetic field]; Kopáček & Karas JPCS(15)-a1412 [inclined black hole magnetosphere].
@ Binaries, and gravitational radiation: Chicone et al CQG(97)gq/96, CQG(99)gq/98; Levin et al PRD(00)gq/99 [homoclinic]; Cornish PRD(01)gq; Cornish & Levin gq/02, PRD(03), CQG(03)gq [time scales]; Wu & Xie PRD(07)-a1004 [chaos not effectively ruled out].
@ Binaries, spinning: Levin PRL(00)gq/99, PRD(03)gq/00; Cornish PRL(00)gq/01; Hughes PRL(00)gq/01 [small effect on radiation]; Schnittman & Rasio PRL(01)gq [numerical, no chaos], comment Cornish & Levin PRL(02)gq; Levin PRD(06)gq [black hole pairs]; Wang & Wu CQG(11) [spin-orbit contributions]; Huang et al EPJC(14)-a1403 [with next-to-leading order spin-spin interactions].
@ Black hole with matter disk: Saa & Venegeroles PLA(99)gq; Saa PLA(00)gq.
@ Many-body systems: El-Zant & Gurzadyan PhyD(98)ap; Sideris & Kandrup PRE(02)ap/01; Burnell et al PRE(04)gq/03 [three-body]; news sn(20)apr [three black holes]; > s.a. gravitational thermodynamics and phenomenology.

Consequences > s.a. chaos.
@ Scattering: Ellis & Tavakol CQG(94), Fukushige et al ApJL(94)ap [and cmb]; Levin PRD(99)ap/98 [light].

Other Systems > see chaos in bianchi models, and in the metric.

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