We present a detailed comparison of several integration schemes applied
to the dynamic system consisting of a charged particle on the Kerr
background endowed with the axisymmetric electromagnetic test field. In
particular, we compare the performance of the symplectic integrator with
several non-symplectic routines and discuss under which circumstances we
should choose the symplectic one and when we should switch to some other
scheme. We are basically concerned with two crucial, yet opposing
aspects - accuracy of the integration and CPU time consumption. The
latter is generally less critical in our application while the highest
possible accuracy is strongly demanded.
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To test the role of large-scale magnetic fields in accretion processes, we study the dynamics of the charged test particles in the vicinity of a black hole immersed into an asymptotically uniform magnetic field. Using the Hamiltonian formalism of the charged particle dynamics, we examine chaotic scattering in the effective potential related to the black hole gravitational field combined with the uniform magnetic field. Energy interchange between the translational and oscillatory modes of the charged particle dynamics provides a mechanism for charged particle acceleration along the magnetic field lines. This energy transmutation is an attribute of the chaotic charged particle dynamics in the combined gravitational and magnetic fields only, the black hole rotation is not necessary for such charged particle acceleration. The chaotic scatter can cause a transition to the motion along the magnetic field lines with small radius of the Larmor motion or vanishing Larmor radius, when the speed of the particle translational motion is largest and it can be ultra-relativistic. We discuss the consequences of the model of ionization of test particles forming a neutral accretion disc, or heavy ions following off-equatorial circular orbits, and we explore the fate of heavy charged test particles after ionization where no kick of heavy ions is assumed and only the switch-on effect of the magnetic field is relevant. We demonstrate that acceleration and escape of the ionized particles can be efficient along the Kerr black hole symmetry axis parallel to the magnetic field lines. We show that a strong acceleration of the ionized particles to ultra-relativistic velocities is preferred in the direction close to the magnetic field lines. Therefore, the process of ionization of Keplerian discs around the Kerr black holes can serve as a model of relativistic jets.
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We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the performance of the symplectic integrator with several non-symplectic routines and discuss under which circumstances we should choose the symplectic one and when we should switch to some other scheme. We are basically concerned with two crucial, yet opposing aspects - accuracy of the integration and CPU time consumption. The latter is generally less critical in our application while the highest possible accuracy is strongly demanded.
Read More
In this paper, we study circular geodesic motion of test particles and
photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing
spherically symmetric regular black-hole or no-horizon spacetimes. While
the Bardeen geometry is not exact solution of Einstein's equations, the
ABG spacetime is related to self-gravitating charged sources governed by
Einstein's gravity and nonlinear electrodynamics. They both are
characterized by the mass parameter m and the charge parameter g. We
demonstrate that in similarity to the Reissner-Nordstrom (RN) naked
singularity spacetimes an antigravity static sphere should exist in all
the no-horizon Bardeen and ABG solutions that can be surrounded by a
Keplerian accretion disc. However, contrary to the RN naked singularity
spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can
contain also an additional inner Keplerian disc hidden under the static
antigravity sphere. Properties of the geodesic structure are reflected
by simple observationally relevant optical phenomena. We give silhouette
of the regular black-hole and no-horizon spacetimes, and profiled
spectral lines generated by Keplerian rings radiating at a fixed
frequency and located in strong gravity region at or nearby the
marginally stable circular geodesics. We demonstrate that the profiled
spectral lines related to the regular black-holes are qualitatively
similar to those of the Schwarzschild black-holes, giving only small
quantitative differences. On the other hand, the regular no-horizon
spacetimes give clear qualitative signatures of their presence while
compared to the Schwarschild spacetimes. Moreover, it is possible to
distinguish the Bardeen and ABG no-horizon spacetimes, if the
inclination angle to the observer is known.
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We study the shadow of the rotating black hole with quintessential
energy i) in vacuum and ii) in the presence of plasma with radial
power-law density. For vacuum case the quintessential field parameter of
the rotating black hole sufficiently changes the shape of the shadow.
With the increasing the quintessential field parameter the radius of the
shadow also increases. With the increase of the radius of the shadow of
the rotating black hole the quintessential field parameter causes
decrease of the distortion of the shadow shape: In the presence of the
quintessential field parameter the shadow of fast rotating black hole
starting to become more close to circle. The shape and size of shadow of
quintessential rotating black hole surrounded by plasma depends on i)
plasma parameters, ii) black hole spin and iii) quintessential field
parameter. With the increase of the plasma refraction index the apparent
radius of the shadow increases. However, for the big values of the
quintessential field parameter the change of the black hole shadow's
shape due to the presence of plasma is not sufficient. In other words:
the effect of the quintessential field parameter becomes more dominant
with compare to the effect of plasma.
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Quintessential dark energy with density $rho$ and pressure $p$ is
governed by an equation of state of the form $p=-omega_{q}rho$ with
the quintessential parameter $omega_qin(-1;-1/3)$. We derive the
geometry of quintessential rotating black holes, generalizing thus the
Kerr spacetimes. Then we study the quintessential rotating black hole
spacetimes with the special value of $omega_q = -2/3$ when the
resulting formulae are simple and easily tractable. We show that such
special spacetimes can exist for dimensionless quintessential parameter
$c<1/6$ and determine the critical rotational parameter $a_0$
separating the black hole and naked singularity spacetime in dependence
on the quintessential parameter $c$. For the spacetimes with $omega_q =
2/3$ we present the integrated geodesic equations in separated form and
study in details the circular geodetical orbits. We give radii and
parameters of the photon circular orbits, marginally bound and
marginally stable orbits. We stress that the outer boundary on the
existence of circular geodesics, given by the so called static radius
where the gravitational attraction of the black hole is balanced by the
cosmic repulsion, does not depend on the dimensionless spin of the
rotating black hole, similarly to the case of the Kerr-de Sitter
spacetimes with vacuum dark energy. We also give restrictions on the
dimensionless parameters $c$ and $a$ of the spacetimes allowing for
existence of stable circular geodesics.
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We investigate a model of a ringed accretion disk, made up by several
rings rotating around a supermassive Kerr black hole attractor. Each
toroid of the ringed disk is governed by the general relativity
hydrodynamic Boyer condition of equilibrium configurations of rotating
perfect fluids. Properties of the tori can then be determined by an
appropriately defined effective potential reflecting the background Kerr
geometry and the centrifugal effects. The ringed disks could be created
in various regimes during the evolution of matter configurations around
supermassive black holes. Therefore, both corotating and counterrotating
rings have to be considered as being a constituent of the ringed disk.
We provide constraints on the model parameters for the existence and
stability of various ringed configurations and discuss occurrence of
accretion onto the Kerr black hole and possible launching of jets from
the ringed disk. We demonstrate that various ringed disks can be
characterized by a maximum number of rings. We present also a
perturbation analysis based on evolution of the oscillating components
of the ringed disk. The dynamics of the unstable phases of the ringed
disk evolution seems to be promising in relation to high-energy
phenomena demonstrated in active galactic nuclei.
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In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.
Read More
We study the shadow of the rotating black hole with quintessential energy i) in vacuum and ii) in the presence of plasma with radial power-law density. For vacuum case the quintessential field parameter of the rotating black hole sufficiently changes the shape of the shadow. With the increasing the quintessential field parameter the radius of the shadow also increases. With the increase of the radius of the shadow of the rotating black hole the quintessential field parameter causes decrease of the distortion of the shadow shape: In the presence of the quintessential field parameter the shadow of fast rotating black hole starting to become more close to circle. The shape and size of shadow of quintessential rotating black hole surrounded by plasma depends on i) plasma parameters, ii) black hole spin and iii) quintessential field parameter. With the increase of the plasma refraction index the apparent radius of the shadow increases. However, for the big values of the quintessential field parameter the change of the black hole shadow's shape due to the presence of plasma is not sufficient. In other words: the effect of the quintessential field parameter becomes more dominant with compare to the effect of plasma.
Read More
Quintessential dark energy with density $rho$ and pressure $p$ is governed by an equation of state of the form $p=-omega_{q}rho$ with the quintessential parameter $omega_qin(-1;-1/3)$. We derive the geometry of quintessential rotating black holes, generalizing thus the Kerr spacetimes. Then we study the quintessential rotating black hole spacetimes with the special value of $omega_q = -2/3$ when the resulting formulae are simple and easily tractable. We show that such special spacetimes can exist for dimensionless quintessential parameter $c<1/6$ and determine the critical rotational parameter $a_0$ separating the black hole and naked singularity spacetime in dependence on the quintessential parameter $c$. For the spacetimes with $omega_q = 2/3$ we present the integrated geodesic equations in separated form and study in details the circular geodetical orbits. We give radii and parameters of the photon circular orbits, marginally bound and marginally stable orbits. We stress that the outer boundary on the existence of circular geodesics, given by the so called static radius where the gravitational attraction of the black hole is balanced by the cosmic repulsion, does not depend on the dimensionless spin of the rotating black hole, similarly to the case of the Kerr-de Sitter spacetimes with vacuum dark energy. We also give restrictions on the dimensionless parameters $c$ and $a$ of the spacetimes allowing for existence of stable circular geodesics.
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