Chaos in pseudo-Newtonian black holes with halos

Guéron, Eduardo; Letelier, Patrício S.

doi:10.1051/0004-6361:20010018

Cited by 29 publications

(31 citation statements)

References 10 publications

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“…We also show the orbital frequency at the ISCO as a function of q, computed using Eq. (16). For spacetimes with spin, the behavior is qualitatively similar, but there are now two ISCO radii, corresponding to prograde and retrograde orbits, respectively.…”

Section: B Innermost Stable Circular Orbitmentioning

confidence: 77%

“…Ergodic motion has been found in other exact relativistic spacetimes by other authors, although these investigations were not carried out in the context of their observable consequences for EMRI detections. Sota, Suzuki, and Maeda [14] described chaotic motion in the Zipoy-Voorhees-Weyl and Curzon spacetimes; Letelier and Viera [15] found chaotic motion around a Schwarzschild black hole perturbed by gravitational waves; Guéron and Letelier observed chaotic motion in a black-hole spacetime with a dipolar halo [16] and in prolate Erez-Rosen bumpy spacetimes [17]; and Dubeibe, Pachon, and Sanabria-Gomez found that some oblate spacetimes which are deformed generalizations of the Tomimatsu-Sato spacetime could also exhibit chaotic motion [18]. The new features of our current results are the presence of potentially ergodic regions for a wider range of magnitudes of the perturbation, and an examination of whether the ergodic regions are astrophysically relevant.…”

Section: Introductionmentioning

confidence: 99%

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Observable properties of orbits in exact bumpy spacetimes

2008

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We explore the properties of test-particle orbits in bumpy spacetimes -stationary, reflectionsymmetric, asymptotically flat solutions of Einstein equations that have a non-Kerr (anomalous) higher-order multipole-moment structure but can be tuned arbitrarily close to the Kerr metric. Future detectors should observe gravitational waves generated during inspirals of compact objects into supermassive central bodies. If the central body deviates from the Kerr metric, this will manifest itself in the emitted waves. Here, we explore some of the features of orbits in non-Kerr spacetimes that might lead to observable signatures. As a basis for this analysis, we use a family of exact solutions proposed by Manko and Novikov which deviate from the Kerr metric in the quadrupole and higher moments, but we also compare our results to other work in the literature. We examine isolating integrals of the orbits and find that the majority of geodesic orbits have an approximate fourth constant of the motion (in addition to the energy, angular momentum, and rest mass) and the resulting orbits are triperiodic to high precision. We also find that this fourth integral can be lost for certain orbits in some oblately deformed Manko-Novikov spacetimes, leading to ergodic motion. However, compact objects will probably not end up on these chaotic orbits in nature. We compute the location of the innermost stable circular orbit (ISCO) and find that the behavior of an orbit in the approach to the ISCO can be qualitatively different depending on whether the location of the ISCO is determined by the onset of an instability in the radial or vertical direction. Finally, we compute periapsis and orbital-plane precessions for nearly circular and nearly equatorial orbits in both the strong and weak field, and discuss weak-field precessions for eccentric equatorial orbits.

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Section: B Innermost Stable Circular Orbitmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Observable properties of orbits in exact bumpy spacetimes

2008

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“…However, realistic astrophysical objects cannot be described very well by Schwarzschild or Kerr metric because of accretion discs or mass deformation existing. About the case of accretion discs, some authors have discussed it in many papers (Letelier et al [20][21][22][23], Wu et al [24], and references in them). In the present paper, we focus on the case of deformation and introduce it briefly as below.…”

Section: Introductionmentioning

confidence: 99%

Revised research about chaotic dynamics in Mankoet al.spacetime

Han

2008

Phys. Rev. D

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A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Goméz, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.

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“…Guéron & Letelier (2001) compared the free-motion dynamics around a Schwarzschild black hole and around a Newtonian point centre, when superposed with a dipolar field. They observed that the black-hole system became more chaotic (than the exact case) when the centre was simulated by the Paczyński-Wiita pseudo-potential, mainly if incorporating special relativistic equation of motion.…”

Section: Previous Results From the Literaturementioning

confidence: 99%

Free motion around black holes with discs or rings: between integrability and chaos – IV

Witzany

Semerák

Suková

2015

Monthly Notices of the Royal Astronomical Society

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The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is considered to test whether the often employed "pseudo-Newtonian" approach (resorting to Newtonian dynamics in gravitational potentials modified to mimic the black-hole field) can reproduce phase-space properties observed in the relativistic treatment. By plotting Poincaré surfaces of section and using two recurrence methods for similar situations as in the relativistic case, we find similar tendencies in the evolution of the phase portrait with parameters (mainly with mass of the disc/ring and with energy of the orbiters), namely those characteristic to weakly non-integrable systems. More specifically, this is true for the Paczyński-Wiita and a newly suggested logarithmic potential, whereas the Nowak-Wagoner potential leads to a different picture. The potentials and the exact relativistic system clearly differ in delimitation of the phase-space domain accessible to a given set of particles, though this mainly affects the chaotic sea whereas not so much the occurrence and succession of discrete dynamical features (resonances). In the pseudoNewtonian systems, the particular dynamical features generally occur for slightly smaller values of the perturbation parameters than in the relativistic system, so one may say that the pseudo-Newtonian systems are slightly more prone to instability. We also add remarks on numerics (a different code is used than in previous papers), on the resemblance of dependence of the dynamics on perturbing mass and on orbital energy, on the difference between the Newtonian and relativistic Bach-Weyl rings, and on the relation between Poincaré sections and orbital shapes within the meridional plane.

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Chaos in pseudo-Newtonian black holes with halos

Cited by 29 publications

References 10 publications

Observable properties of orbits in exact bumpy spacetimes

Observable properties of orbits in exact bumpy spacetimes

Revised research about chaotic dynamics in Mankoet al.spacetime

Free motion around black holes with discs or rings: between integrability and chaos – IV

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