Lyapunov indices with two nearby trajectories in a curved spacetime

Wu, Xiaoxia; Huang, Tian-Yi; Zhang, H.

doi:10.1103/physrevd.74.083001

Cited by 123 publications

(116 citation statements)

References 30 publications

(63 reference statements)

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“…The fact that geodesic motion in MSM background exhibits chaotic behavior was shown in [31][32][33] mainly by studying Poincaré sections, but also by applying the FLI indicator [19] as defined in [16], and by the means of frequency analysis [33].…”

Section: Geodesic and Geodesic Deviationmentioning

confidence: 99%

“…(11), (15), we have to ensure that ξ α and Dξ α dτ will remain spacelike. The prescription for this [15,16] is to choose initial conditions for ξ α , Dξ α dτ such that…”

Section: Chaotic Indicatorsmentioning

confidence: 99%

“…For the geodesic motion in curved spacetimes, which is the case we focus on, some suggestions to solve the above issues have already been provided. For instance, the indicators can be evaluated by applying the 3 + 1 spacetime splitting approach [17] or by choosing the proper time as the time parameter [15] and using the invariant measure of the deviation vector either derived by the geodesic deviation equations [15] or by the two nearby orbits approximation [16]. In this study, the guideline of Sota et al [15] was preferred for adjusting the chaotic indicators to the GR framework.…”

Section: Introductionmentioning

confidence: 99%

“…However, the definition and the efficiency of these indicators pose issues in the framework of General Relativity (GR) (see, e.g., [14,16] and references therein). Namely, one has to redefine the chaotic indicators in such a way * Electronic address: gglukes@gmail.com that they will be invariant under coordinate transformations, and then to test these redefined indicators for their ability to detect chaos.…”

Section: Introductionmentioning

confidence: 99%

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Adjusting chaotic indicators to curved spacetimes

Lukes-Gerakopoulos¹

2014

Phys. Rev. D

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In this work, chaotic indicators, which have been established in the framework of classical mechanics, are reformulated in the framework of general relativity in such a way that they are invariant under coordinate transformation. For achieving this, the prescription for reformulating mLCE given by [Y. Sota, S. Suzuki, and K.-I. Maeda, Classical Quantum Gravity 13, 1241 (1996)] is adopted. Thus, the geodesic deviation vector approach is applied, and the proper time is utilized as measure of time. Following the aforementioned prescription, the chaotic indicators FLI, MEGNO, GALI, and APLE are reformulated. In fact, FLI has been reformulated by adapting other prescriptions in the past, but not by adapting the Sota et al. one. By using one of these previous reformulations of FLI, an approximative expression giving MEGNO as function of FLI has been applied on non-integrable curved spacetimes in a recent work. In the present work the reformulation of MEGNO is provided by adjusting the definition of the indicator to the Sota et al. prescription. GALI, and APLE are reformulated in the framework of general relativity for the first time. All the reformulated indicators by the Sota et al. prescription are tested and compared for their efficiency to discern order from chaos.

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Section: Geodesic and Geodesic Deviationmentioning

confidence: 99%

“…(11), (15), we have to ensure that ξ α and Dξ α dτ will remain spacelike. The prescription for this [15,16] is to choose initial conditions for ξ α , Dξ α dτ such that…”

Section: Chaotic Indicatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adjusting chaotic indicators to curved spacetimes

Lukes-Gerakopoulos¹

2014

Phys. Rev. D

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“…[32] for a discussion in the context of general relativity). Non-minimal coupling contributes to this through F µ -dependent terms.…”

Section: World-line Deviationsmentioning

confidence: 99%

Non-geodesic motion in f(G) gravity with non-minimal coupling

Mohseni

2009

Physics Letters B

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The dynamics of test particles in f (G) modified Gauss-Bonnet gravity is investigated. It is shown that in f (G) gravity models with non-minimal coupling to matter, particles experience an extra force normal to their four-velocities and as a result move along non-geodesic world-lines. The explicit form of the extra force depends on the function of the Gauss-Bonnet term included in coupling term. The effects of this force on the relative accelerations of particles are studied.

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Effect of the Quadrupole–Monopole Interaction on Chaos in Compact Binaries

Liang

2019

Annalen der Physik

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The dynamics of a post‐Newtonian Lagrangian of spinning compact binaries, including the Newtonian, post‐Newtonian, spin‐orbit, spin‐spin, and quadrupole–monopole interaction contributions are investigated herein. According to the Euler–Lagrangian equations, exact and approximate equations of motion can be written. Numerical computations show that the constants of motion can reach satisfactory accuracies in the exact equations but rather poor accuracies in the approximate equations. Similar to the spin–orbit coupling or the spin–spin coupling, the quadrupole–monopole interaction plays a role in some spin effects that lead to the precession of orbits. With the increase in quadrupole–monopole and extension of integration, the orbits precess strongly and the difference in the precession of orbits between the two sets of equations increases. The quadrupole–monopole interaction can also cause the chaoticity of spinning compact binaries. When it increases, chaos is strong under some circumstances in the exact equations but not in the approximate equations.

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Lyapunov indices with two nearby trajectories in a curved spacetime

Cited by 123 publications

References 30 publications

Adjusting chaotic indicators to curved spacetimes

Adjusting chaotic indicators to curved spacetimes

Non-geodesic motion in f(G) gravity with non-minimal coupling

Effect of the Quadrupole–Monopole Interaction on Chaos in Compact Binaries

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