Chaotic Motion in Multi-Black Hole Spacetimes and Holographic Screens

Hanan, W. G.; Radu, Eugen

doi:10.1142/s0217732307022815

Cited by 34 publications

(31 citation statements)

References 19 publications

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“…The approximated motion of photons in this field shows chaotic features: the boundary between capture, orbital and escape basins is fractal, becoming a self‐similar Cantor set in the limit of infinite distance between the centres, with its box‐counting dimension falling off logarithmically. Hanan & Radu (2007) recently generalized the problem of multiple extreme black holes to higher dimensional space–times (with special attention to the five‐dimensional case) and found qualitative similarity of chaos in test dynamics there.…”

Section: Dynamics Of Test Motion In Black Hole Fieldsmentioning

confidence: 99%

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

Semerák¹,

Suková²

2010

Monthly Notices of the Royal Astronomical Society

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Geodesic dynamics is regular in the fields of isolated stationary black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here, we examine what amount of stochasticity is induced in Schwarzschild space–time by the presence of an additional source. Following astrophysical motivation, we specifically consider thin rings or discs lying symmetrically around the hole, and describe the total field in terms of exact static and axially symmetric solutions of Einstein's equations. The growth of chaos in time‐like geodesic motion is illustrated on Poincaré sections, on time series of position or velocity and their Fourier spectra, and on time evolution of the orbital ‘latitudinal action’. The results are discussed in terms of dependence on the mass and position of the ring/disc and on geodesic parameters (energy and angular momentum). In the Introduction, we also add an overview of the literature.

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Section: Dynamics Of Test Motion In Black Hole Fieldsmentioning

confidence: 99%

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

Semerák¹,

Suková²

2010

Monthly Notices of the Royal Astronomical Society

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“…In black hole physics, the chaotic orbits of particles have been found to exist in multi-black hole spacetime [4,5], in the Manko-Novikov black hole spacetime [6][7][8][9][10], in the perturbed Schwarzschild spacetime [11][12][13][14] , in the spacetime of a black hole immersed an external magnetic field [15] and in the accelerating and rotating black holes spacetime [16]. Moreover, it is of interest to find that the chaotic behaviors appear in ring string dynamics in the Schwarzschild black hole spacetime [17] and in AdS black hole spacetimes [18,19].…”

Section: Introductionmentioning

confidence: 99%

Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

2020

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We have studied thermal chaotic behavior in the extended phase space for a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos.Our result show that for the temporal perturbation the thermal chaos in the charged dilaton-AdS black hole occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude.These behaviors are similar to those in other AdS black hole, which can be regarded as the common features of the static AdS black holes. Moreover, we also find that the critical temporal perturbation amplitude leading to chaos increases with the dilaton parameter and decreases with the charge. This means that under the temporal perturbation the presence of dilaton parameter makes the onset of chaos more difficult, which differs from that of the charge parameter.

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“…1. Chaotic scattering in GR spacetimes has been observed and discussed in binary or multi-BH solutions (see, e.g., [45,46,[74][75][76][77][78][79][80][81][82][83][84]) and is well known in the context of manybody scattering in classical dynamics, for example, the scattering of charged particles off magnetic dipoles [85] and the three-body problem (see, e.g., [86]). KBHsSH or RBSs provide an example of chaos in geodesic motion on the background of a single compact object, which moreover solves a simple and well-defined matter model minimally coupled to GR.…”

Section: Introductionmentioning

confidence: 99%

Chaotic lensing around boson stars and Kerr black holes with scalar hair

et al. 2016

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In a recent paper [P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, Phys. Rev. Lett. 115, 211102 (2015).], it was shown that the lensing of light around rotating boson stars and Kerr black holes with scalar hair can exhibit chaotic patterns. Since no separation of variables is known (or expected) for geodesic motion on these backgrounds, we examine the 2D effective potentials for photon trajectories, to obtain a deeper understanding of this phenomenon. We find that the emergence of stable light rings on the background spacetimes allows the formation of "pockets" in one of the effective potentials, for open sets of impact parameters, leading to an effective trapping of some trajectories, dubbed "quasibound orbits." We conclude that pocket formation induces chaotic scattering, although not all chaotic orbits are associated to pockets. These and other features are illustrated in a gallery of examples, obtained with a new ray-tracing code, PYHOLE, which includes tools for a simple, simultaneous visualization of the effective potential, together with the spacetime trajectory, for any given point in a lensing image. An analysis of photon orbits allows us to further establish a positive correlation between photon orbits in chaotic regions and those with more than one turning point in the radial direction; we recall that the latter is not possible around Kerr black holes. Moreover, we observe that the existence of several light rings around a horizon (several fundamental orbits, including a stable one), is a central ingredient for the existence of multiple shadows of a single hairy black hole. We also exhibit the lensing and shadows by Kerr black holes with scalar hair, observed away from the equatorial plane, obtained with PYHOLE.

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Chaotic Motion in Multi-Black Hole Spacetimes and Holographic Screens

Cited by 34 publications

References 19 publications

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

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

Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

Chaotic lensing around boson stars and Kerr black holes with scalar hair

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