Chaotic motion in axially symmetric potentials with oblate quadrupole deformation

Letelier, Patrício S.; Ramos-Caro, Javier; López-Suspes, Framsol

doi:10.1016/j.physleta.2011.08.050

Cited by 9 publications

(9 citation statements)

References 15 publications

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“…By using the Melnikov integral method adapted for parabolic orbits [11], we prove that the Hamiltonian flow on the zero-energy manifold for the Kepler problem perturbed by a quadrupole moment is chaotic, irrespective of the perturbation being of prolate or oblate type. This result favors, in this way, the numerical results obtained in [9], which are in conflict with those ones presented in [4].…”

Section: Final Remarkssupporting

confidence: 42%

“…This qualitative differences for the cases q > 0 and q < 0 is attributed in [4] to some qualitative differences in the saddle points of the effective potential, but it is also known that such kind of local argument leads typically to conditions that are not sufficient neither necessary to the appearance of chaos in theses systems [8]. More recently, a new numerical study suggesting that the oblate perturbations would also give origin to bounded chaotic orbits has appeared [9]. Here, we explore these conflicting results by applying the Melnikov integral method [10] for the parabolic orbits [11] (the zero-energy manifold) of (1).…”

Section: Introductionmentioning

confidence: 99%

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Chaos in the Kepler Problem with Quadrupole Perturbations

Depetri¹,

Saa²

2015

Geometry, Mechanics, and Dynamics

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Section: Final Remarkssupporting

confidence: 42%

Section: Introductionmentioning

confidence: 99%

Chaos in the Kepler Problem with Quadrupole Perturbations

Depetri¹,

Saa²

2015

Geometry, Mechanics, and Dynamics

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“…They found there is a close connection between linear stability/instability of equatorial circular orbits and regularity/chaoticity of general three-dimensional orbits passing through their radii. 4 The same group (Letelier et al 2011) also revisited geodesic dynamics in the system composed of a monopole or an isotropic harmonic oscillator and oblate quadrupole, and found several new features not noticed before. Wang & Wu (2011) employed a pseudo-Newtonian potential in order to superpose a rotating black hole with a quadrupole halo.…”

Section: Discussionmentioning

confidence: 90%

Free motion around black holes with discs or rings: between integrability and chaos - II

Semerák

Suková

2012

Monthly Notices of the Royal Astronomical Society

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We continue the study of time-like geodesic dynamics in exact static, axially and reflection symmetric space-times describing the fields of a Schwarzschild black hole surrounded by thin discs or rings. In the previous paper, the rise (and decline) of geodesic chaos with ring/disc mass and position and with test particle energy was revealed on Poincaré sections, on time series of position or velocity and their power spectra, and on time evolution of the orbital 'latitudinal action'. In agreement with the KAM theory of nearly integrable dynamical systems and with the results observed in similar gravitational systems in the literature, we found orbits of very different degrees of chaoticity in the phase space of perturbed fields. Here we compare selected orbits in more detail and try to classify them according to the characteristics of the corresponding phase-variable time series, mainly according to the shape of the time-series power spectra, and also applying two recurrence methods: the method of 'average directional vectors', which traces the directions in which the trajectory (recurrently) passes through a chosen phase-space cell, and the 'recurrence-matrix' method, which consists of statistics over the recurrences themselves. All the methods proved simple and powerful, while it is interesting to observe how they differ in sensitivity to certain types of behaviour.

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“…If the central object is a Kerr black hole, the no-hair theorems [6][7][8] for electricallyneutral, isolated black holes imply that all the multipole moments of the source are uniquely and fully characterized by the mass and the spin angular momentum of the source. Due to the particular features of the Kerr solution, evidence of black holes outside general relativity, containing higher-order independent multipole moments, would lead to a change of paradigm in gravitational physics [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Stealth chaos due to frame-dragging

Gutierrez

Cárdenas-Avendaño

Yunes

et al. 2021

Class. Quantum Grav.

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While the geodesic motion around a Kerr black hole is fully integrable and therefore regular, numerical explorations of the phase-space around other spacetime configurations, with a different multipolar structure, have displayed chaotic features. In most of these solutions, the role of the purely general relativistic effect of frame-dragging in chaos has eluded a definite answer. In this work, we show that, when considering neutral test particles around a family of stationary axially-symmetric analytical exact solution to the Einstein–Maxwell field equations, frame-dragging (as captured through spacetime vorticity) is capable of reconstructing KAM-tori from initially highly chaotic configurations. We study this reconstruction by isolating the contribution of the spacetime vorticity scalar to the dynamics, and exemplify our findings by computing rotation curves and the dimensionality of phase-space. Since signatures of chaotic dynamics in gravitational waves have been suggested as a way to test general relativity in the strong-field regime, we have computed gravitational waveforms using the semi-relativistic approximation and studied the frequency content of the gravitational wave spectrum. If this mechanism is generic, chaos suppression by frame-dragging may undermine present proposals to verify the hypothesis of the no-hair theorems and the validity of general relativity.

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Chaotic motion in axially symmetric potentials with oblate quadrupole deformation

Cited by 9 publications

References 15 publications

Chaos in the Kepler Problem with Quadrupole Perturbations

Chaos in the Kepler Problem with Quadrupole Perturbations

Free motion around black holes with discs or rings: between integrability and chaos - II

Stealth chaos due to frame-dragging

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