scholarly journals The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Peter Komorowski ◽  
Sree Valluri ◽  
Martin Houde
Keyword(s):  
Black Hole ◽  
Evolution Equations ◽  
Kerr Black Hole ◽  
Reaction Model ◽  
Back Reaction ◽  
Kerr Spacetime ◽  
System A ◽  
Binary Black Hole ◽  
Maximum Value ◽  
Published Result

AbstractIn an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, i) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q X) for given values of latus rectum (l̃) and eccentricity (e), has been introduced as a laboratory in which the consistency of dQ/dt with corresponding evolution equations for d l̃/dt and de/dt might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of dQ/dt, based only on published formulae for d l̃/dt and de/dt, was performed for elliptical orbits on the abutment. The resulting expression for dQ/dt matched the published result to the second order in e. We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of e and l̃−.

scholarly journals Global embeddings and hydrodynamic properties of Kerr black hole

2016 ◽  
Vol 31 (35) ◽  
pp. 1650204
Author(s):  
Soon-Tae Hong
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Equatorial Plane ◽  
Kerr Black Hole ◽  
Kerr Spacetime ◽  
Stable Circular Orbit ◽  
Massive Particles ◽  
Flat Embedding ◽  
Bound Orbits ◽  
The Impact

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies, we study the black holes GRO J1655-40 and 4U 1543-47 to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of 1.0 ly around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9 + 3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane, we investigate the warp products of the Kerr spacetime.

Dynamics of Magnetized and Magnetically Charged Particles around Regular Nonminimal Magnetic Black Holes

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 71
Author(s):  
Javlon Rayimbaev ◽  
Bakhtiyor Narzilloev ◽  
Ahmadjon Abdujabbarov ◽  
Bobomurat Ahmedov
Keyword(s):  
Black Hole ◽  
Magnetic Charge ◽  
Coupling Parameter ◽  
Charged Particles ◽  
Kerr Black Hole ◽  
Harmonic Oscillations ◽  
Yang Mills ◽  
Keplerian Orbits ◽  
Maximum Value ◽  
Mills Field

The present paper is devoted to the study of the event horizon properties of spacetime around a regular nonminimal magnetic black hole (BH), together with dynamics of magnetized and magnetically charged particles in the vicinity of the BH. It is shown that the minimum value of the outer horizon of the extreme charged BH increases with the increase in coupling parameter. It reaches its maximum value of 1.5M when q→∞, while the maximal value of the BH charge decreases and tends toward zero. We also present a detailed analysis of magnetized particles’ motion around a regular nonminimal magnetic black hole. The particle’s innermost circular stable orbits (ISCOs) radius decreases as the magnetic charge and the parameter β increase and the coupling parameter of Yang–Mills field causes a decrease at the values of the magnetic charge near to its maximum. We show that the magnetic charge can mimic the spin of a rotating Kerr black hole up to the value of a=0.7893M, providing the same value for an ISCO of a magnetized particle with the parameter β=10.2 when the coupling parameter is q=0. Moreover, Lyapunov exponents, Keplerian orbits and harmonic oscillations of magnetized particles motion are also discussed.

Thermal Casimir effect in the Kerr spacetime with quintessence

2019 ◽  
Vol 34 (16) ◽  
pp. 1950125
Author(s):  
V. B. Bezerra ◽  
J. M. Toledo
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Equatorial Plane ◽  
Casimir Effect ◽  
Kerr Black Hole ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Kerr Spacetime

We calculate thermal corrections to the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence, taking into account the metrics derived by Ghosh [S. G. Ghosh, Eur. Phys. J. C 76, 222 (2016)] and Toshmatov et al. [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)]. We compare both results and show that they are almost the same, except very close to the horizons. At [Formula: see text], equatorial plane, the results are the same, as should be expected, due to the fact that the metrics coincide in this region.

scholarly journals Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Wei Sun ◽  
Ying Wang ◽  
Fuyao Liu ◽  
Xin Wu
Keyword(s):  
Black Hole ◽  
Charged Particles ◽  
Kerr Black Hole ◽  
Space Structure ◽  
Point Of View ◽  
Symplectic Integrator ◽  
Spacetime Geometry ◽  
Kerr Spacetime ◽  
Phase Space Structure ◽  
Local Point

AbstractIn a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincaré sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.

scholarly journals Comments on “Casimir effect in the Kerr spacetime with quintessence”

2017 ◽  
Vol 32 (21) ◽  
pp. 1775001 ◽  
Author(s):  
Bobir Toshmatov ◽  
Zdeněk Stuchlík ◽  
Bobomurat Ahmedov
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Casimir Effect ◽  
Kerr Black Hole ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Kerr Spacetime ◽  
The Difference

This comment is devoted to the recalculation of the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence derived in [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)] and its comparison with the results recently obtained in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A 32, 1750005 (2017)] in the spacetime [S. G. Ghosh, Eur. Phys. J. C 76, 222 (2016)]. We have shown that in the more realistic spacetime which does not have the failures illustrated here, the Casimir energy is significantly bigger than that derived in [V. B. Bezerra, M. S. Cunha, L. F. F. Freitas and C. R. Muniz, Mod. Phys. Lett. A 32, 1750005 (2017)], and the difference becomes crucial especially in the regions of near horizons of the spacetime.

scholarly journals INSTABILITIES IN KERR SPACETIMES

2011 ◽  
Vol 20 (supp01) ◽  
pp. 27-31 ◽  
Author(s):  
GUSTAVO DOTTI ◽  
REINALDO J. GLEISER ◽  
IGNACIO F. RANEA-SANDOVAL
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Infinite Family ◽  
Dirac Field ◽  
Cauchy Horizon ◽  
Kerr Spacetime ◽  
Gravitational Perturbations ◽  
Black Hole Interior ◽  
The Stability ◽  
Do So

We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary s = ±1 representing electromagnetic perturbations, s = ±1/2 representing a perturbation by a Dirac field and s = 0 representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.

scholarly journals Weighing the black hole via quasi-local energy

2017 ◽  
Vol 32 (24) ◽  
pp. 1730021 ◽  
Author(s):  
Yuan K. Ha
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Waves ◽  
Kerr Black Hole ◽  
Rotational Energy ◽  
Local Energy ◽  
External Energy ◽  
Event Horizons ◽  
Binary Black Hole ◽  
Asymptotic Values

We set to weigh the black holes at their event horizons in various spacetimes and obtain masses which are substantially higher than their asymptotic values. In each case, the horizon mass of a Schwarzschild, Reissner–Nordström, or Kerr black hole is found to be twice the irreducible mass observed at infinity. The irreducible mass does not contain electrostatic or rotational energy, leading to the inescapable conclusion that particles with electric charges and spins cannot exist inside a black hole. This is proposed as the External Energy Paradigm. A higher mass at the event horizon and its neighborhood is obligatory for the release of gravitational waves in binary black hole merging. We describe how these horizon mass values are obtained in the quasi-local energy approach and applied to the black holes of the first gravitational waves GW150914.

GENERALIZED UNCERTAINTY PRINCIPLE AND THE QUANTUM ENTROPY OF A KERR BLACK HOLE

2004 ◽  
Vol 13 (09) ◽  
pp. 1847-1856 ◽  
Author(s):  
CHEN LI ◽  
LI XIANG ◽  
YOU-GEN SHEN
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Kerr Black Hole ◽  
Quantum States ◽  
Brick Wall ◽  
Wall Model ◽  
Kerr Spacetime ◽  
Brick Wall Model ◽  
New Equation

Taking into account the generalized uncertainty principle (GUP), we calculate the entropy of a scalar field in a Kerr spacetime. Different to previous work, we have used an new equation of the density of quantum states, which arises from the modified commutation relation [Formula: see text]. The divergence in the brick wall model is removed, without the cutoff.

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