Free motion around black holes with discs or rings: between integrability and chaos - II
arXiv:1211.4107 · doi:10.1111/j.1365-2966.2012.21630.x
Abstract
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.
22 pages, 14 figures
References in corpus (34)
- Lyapunov indices with two nearby trajectories in a curved spacetime
- Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
- Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
- Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects
- Enhanced activity of massive black holes by stellar capture assisted by a self-gravitating accretion disc
- Resurvey of order and chaos in spinning compact binaries
- The non-integrability of the Zipoy-Voorhees metric
- Relativistic chaos is coordinate invariant
- Free motion around black holes with discs or rings: between integrability and chaos - I
- Chaos and Order in Models of Black Hole Pairs
- On the geometry of Hamiltonian chaos
- Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
- The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
- Global integrability of cosmological scalar fields
- Spacetime Encodings II - Pictures of Integrability
- On highly eccentric stellar trajectories interacting with a self-gravitating disc in Sgr A*
- A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
- Chaos detection tools: application to a self-consistent triaxial model
- Testing the existence of regions of stable orbits at small radii around black hole candidates
- Chaotic motion in multi-black hole spacetimes and holographic screens
- Newtonian and Pseudo-Newtonian Hill Problem
- Carter-like constants of the motion in Newtonian gravity and electrodynamics
- Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
- Star-disc interactions in a galactic centre and oblateness of the inner stellar cluster
- Chaos in Geodesic Motion around a Black Ring
- Dynamics and chaos in the unified scalar field Cosmology
- Stability of Orbits around a Spinning Body in a Pseudo-Newtonian Hill Problem
- Relativistic effects in the chaotic Sitnikov problem
- Relativistic invariance of Lyapunov exponents in bounded and unbounded systems
- Gravitational Wave Signals from Chaotic System: A Point Mass with A Disk
- Escape of photons from two fixed extreme Reissner-Nordström black holes
- 1/f fluctuations in spinning-particle motions around Schwarzschild black hole
- Chaotic motion in Kundt spacetimes
- Homoclinic chaos and energy condition violation