Characterization of Regular and Chaotic Motions

Lakshmanan, M.; Rajasekar, S.

doi:10.1007/978-3-642-55688-3_8

Cited by 1 publication

(3 citation statements)

References 19 publications

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“…The chaotic features displayed in the rotation curve can sometimes be hard to discern by naked eye, due to subtle changes in the monotonicity of the curve. As an alternative, it is possible to focus on the dimension of the invariant manifold in which the motion takes place, as conservative chaotic systems have an integer dimension of the invariant manifolds, whereas the dissipative have a non-integer dimension [41].…”

Section: Figures Of Merit: the Rotation Number And The Correlation Di...mentioning

confidence: 99%

“…Among different proposals for measuring the invariant-manifold dimension [41], we focused on the correlation dimension introduced by Grassberger and Procaccia in reference [40]. In this approach, the phase-space distance 1 and the correlation dimension C ( ) is proportional to D , where D is the dimensionality of the phase-space orbit.…”

Section: Figures Of Merit: the Rotation Number And The Correlation Di...mentioning

confidence: 99%

“…Orbits with D = 1 are close to the invariant point or to small Bifkhoff islands that surround periodic orbits, while orbits with D = 2 or 3 are integrable [41].…”

Section: Figures Of Merit: the Rotation Number And The Correlation Di...mentioning

confidence: 99%

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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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Section: Figures Of Merit: the Rotation Number And The Correlation Di...mentioning

confidence: 99%

Section: Figures Of Merit: the Rotation Number And The Correlation Di...mentioning

confidence: 99%