Small oscillations of current-carrying string loops around stable
equilibrium positions corresponding to minima of the effective potential
in the equatorial plane of the Kerr black holes are studied using the
perturbation method. In the lowest approximation, two uncoupled harmonic
oscillators are obtained that govern the radial and vertical
oscillations; the higher-order terms determine nonlinear phenomena and
transition to chaotic motion through quasiperiodic stages of the
oscillatory motion. The radial profiles of frequencies of the radial and
vertical harmonic oscillations that are also relevant in the
quasiperiodic stages of the oscillatory motion are given, and their
properties, independent of the spin of the black holes and the angular
momentum and tension of the string loops, are determined. It is shown
that the radial profiles differ substantially from those corresponding
to the radial and vertical frequencies of the geodetical epicyclic
motion; however, they have the same mass scaling and their magnitude is
of the same order. Therefore, we are able to demonstrate that, assuming
the relevance of resonant phenomena of radial and vertical string-loop
oscillations at their frequency ratio 3∶2, the oscillatory
frequencies of string loops can be related to the frequencies of the
twin high-frequency quasiperiodic oscillations (HF QPOs) observed in the
microquasars GRS 1915+105, XTE 1550-564, GRO 1655-40. We can conclude
that oscillating current-carrying string loops have to be considered as
one of the possible explanations of the HF QPOs occurring in the field
of compact objects.
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We demonstrate that the cosmological constant substantially influences motion of both Magellanic Clouds in the gravitational field of Milky Way.
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Equatorial circular orbits of test particles in the Kerr-anti-de Sitter black-hole and naked-singularity spacetimes are analyzed and their properties like the existence, orientation and stability are discussed. Due to the attractive cosmological constant (), all particles moving along equatorial orbits are still bound in the gravitational field of the central object. In general, there are two families of equatorial circular orbits. Particles moving along minus-family orbits possess negative angular momentum and, thus, they are counterrotating from the point of view of the locally non-rotating frames (LNRF). Particles moving along plus-family orbits possess, in most cases, positive angular momentum and belong to corotating particles from the point of view of the LNRF. Nevertheless, in stationary regions inside black holes and also near naked singularities with appropriately chosen value of the cosmological constant and rotational parameter , there are also counterrotating plus-family circular orbits. Moreover, in spacetimes with , some of these orbits are characterized by negative specific energy, indicating the bounding energy of the particle, moving along such an orbit, higher than its rest energy. In black-hole spacetimes, all such orbits are radially unstable, but in naked-singularity spacetimes, stable counterrotating orbits with negative specific energy exist.
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It has been recently shown that the cosmic repulsion can have a highly significant influence on the motion of Magellanic Clouds (MC) in the gravitational field of Milky Way, treated in the framework of the Cold Dark Matter (CDM) halo model. However, there is an alternative to the CDM halo explanation of the rotation curves in the periphery of spiral galaxies, based on MOdified Newtonian Dynamics (MOND). Therefore, we study the role of the cosmic repulsion in the framework of the MOND theory applied to determine the MC motion. Our results demonstrate that in the MOND framework the influence of the cosmic repulsion on the motion of both Small and Large MC is also highly significant, but it is of a different character than in the framework of the CDM halo model. Moreover, we demonstrate that the MC motion in the framework of the CDM halo and MOND models is subtantially different and can serve as a test of these fundamentally different approaches to the explanation of the phenomena related to galaxies and the motion of satellite galaxies.
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The particle acceleration mechanism in S2×R1 topology, namely, in the spacetime of the five-dimensional compact black string, has been studied. The expression of center-of-mass energy of the colliding neutral particles near static black string has been found. The collision of a charged particle moving at the innermost stable circular orbit with a neutral particle coming from infinity has been considered when black string is immersed in external uniform magnetic field. It has been shown that the unlimited center-of-mass energy can be approached in the case of the extremal rotation of the black string which is similar to the analogous effect in Kerr spacetime. We have also obtained that the scattering energy of particles in the center-of-mass system can take arbitrarily large values not only for extremal black string but also for the nonextremal one. It has been derived that the presence of the extra dimension can, in principle, increase the upper limit of efficiency of energy extraction from the extremely rotating black string up to 203% versus 143% which can be extracted from the extreme Kerr black hole.
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Equatorial circular orbits of test particles in the Kerr-anti-de Sitter
black-hole and naked-singularity spacetimes are analyzed and their
properties like the existence, orientation and stability are discussed.
Due to the attractive cosmological constant (), all particles moving
along equatorial orbits are still bound in the gravitational field of
the central object. In general, there are two families of equatorial
circular orbits. Particles moving along minus-family orbits possess
negative angular momentum and, thus, they are counterrotating from the
point of view of the locally non-rotating frames (LNRF). Particles
moving along plus-family orbits possess, in most cases, positive angular
momentum and belong to corotating particles from the point of view of
the LNRF. Nevertheless, in stationary regions inside black holes and
also near naked singularities with appropriately chosen value of the
cosmological constant and rotational parameter , there are also
counterrotating plus-family circular orbits. Moreover, in spacetimes
with , some of these orbits are characterized by negative specific
energy, indicating the bounding energy of the particle, moving along
such an orbit, higher than its rest energy. In black-hole spacetimes,
all such orbits are radially unstable, but in naked-singularity
spacetimes, stable counterrotating orbits with negative specific energy
exist.
Read More
It has been recently shown that the cosmic repulsion can have a highly
significant influence on the motion of Magellanic Clouds (MC) in the
gravitational field of Milky Way, treated in the framework of the Cold
Dark Matter (CDM) halo model. However, there is an alternative to the
CDM halo explanation of the rotation curves in the periphery of spiral
galaxies, based on MOdified Newtonian Dynamics (MOND). Therefore, we
study the role of the cosmic repulsion in the framework of the MOND
theory applied to determine the MC motion. Our results demonstrate that
in the MOND framework the influence of the cosmic repulsion on the
motion of both Small and Large MC is also highly significant, but it is
of a different character than in the framework of the CDM halo model.
Moreover, we demonstrate that the MC motion in the framework of the CDM
halo and MOND models is subtantially different and can serve as a test
of these fundamentally different approaches to the explanation of the
phenomena related to galaxies and the motion of satellite galaxies.
Read More
The particle acceleration mechanism in S2×R1
topology, namely, in the spacetime of the five-dimensional compact black
string, has been studied. The expression of center-of-mass energy of the
colliding neutral particles near static black string has been found. The
collision of a charged particle moving at the innermost stable circular
orbit with a neutral particle coming from infinity has been considered
when black string is immersed in external uniform magnetic field. It has
been shown that the unlimited center-of-mass energy can be approached in
the case of the extremal rotation of the black string which is similar
to the analogous effect in Kerr spacetime. We have also obtained that
the scattering energy of particles in the center-of-mass system can take
arbitrarily large values not only for extremal black string but also for
the nonextremal one. It has been derived that the presence of the extra
dimension can, in principle, increase the upper limit of efficiency of
energy extraction from the extremely rotating black string up to 203%
versus 143% which can be extracted from the extreme Kerr black hole.
Read More
The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.
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The possible occurrence of equilibrium off-equatorial tori in the
gravitational and electromagnetic fields of astrophysical compact
objects has been recently proved based on non-ideal magnetohydrodynamic
theory. These stationary structures can represent plausible candidates
for the modeling of coronal plasmas expected to arise in association
with accretion disks. However, accretion disk coronae are formed by a
highly diluted environment, and so the fluid description may be
inappropriate. The question is posed of whether similar off-equatorial
solutions can also be determined in the case of collisionless plasmas
for which treatment based on kinetic theory, rather than a fluid one, is
demanded. In this paper the issue is addressed in the framework of the
Vlasov-Maxwell description for non-relativistic, multi-species
axisymmetric plasmas subject to an external dominant spherical
gravitational and dipolar magnetic field. Equilibrium configurations are
investigated and explicit solutions for the species kinetic distribution
function are constructed, which are expressed in terms of generalized
Maxwellian functions characterized by isotropic temperature and
non-uniform fluid fields. The conditions for the existence of
off-equatorial tori are investigated. It is proved that these levitating
systems are admitted under general conditions when both gravitational
and magnetic fields contribute to shaping the spatial profiles of
equilibrium plasma fluid fields. Then, specifically, kinetic effects
carried by the equilibrium solution are explicitly provided and
identified here with diamagnetic energy-correction and electrostatic
contributions. It is shown that these kinetic terms characterize the
plasma equation of state by introducing non-vanishing deviations from
the assumption of thermal pressure.
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