We discuss in the framework of general relativity the role of the dark
energy represented by the cosmological constant, restricted due to
cosmological tests, in the polytropic models of dark matter halos. The
internal spacetime of the polytropic spheres governs circular geodesic
orbits that can be compared with the velocity curves observed in large
galaxies, indicating the possibility to use for the halo model both non-
relativistic very extended and diluted polytropes, or relativistic
polytropes with nearly critical value of the relativistic parameter
sigma = p_mathrm{c}/varrho_mathrm{c} enabling extremely large polytrope
extension, limited efficiently by the influence of the dark energy to
agree with extension of dark matter halos of large galaxies. We also
show that the so-called trapping relativistic polytropes with extremely
large extension allow for gravitational instability of their central
parts leading to the creation of a supermassive black hole inside of
such an extremely extended polytrope representing galactic halo.
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We discuss the photon motion in the framework of general relativity
coupled to non-linear electrodynamics. Photons no longer follow the
null-geodesics of the spacetime but rather null-geodesics of associated
effective metric. Here we compare structure of circular geodesics and
time-delays of neutrinos in Bardeen spacetimes with those of photons in
effective geometry. We also discuss construction the Keplerian disks
images in the Bardeen spacetimes and compare them with the images of
Keplerian disks in RN spacetime.
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Charged fluids circling in strong central gravitational and ambinet
magnetic fields, characteristic for compact objects backgrounds, can
embody interesting configurations. In contrast to the widely considered
neutral fluid structures imitating thick equatorial accretion discs with
negligible loss of mass, when the fluid is properly charged, we can find
it forming unique toroidal structures `levitating' above the equatorial
plane and also those hovering near the symmetry axis. Along with
analytical topological studies of these structures, we can also present
an survey of their basic physical characteristics, such as pressure,
density and temperature profiles.
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In many astrophysically relevant situations, radiation-reaction forces
acting upon a charge cannot be ignored, and the question of the location
and stability of circular orbits in such a regime arises. The motion of
a point charge with radiation reaction in flat spacetime is described by
the Lorenz-Dirac (LD) equation, while in curved spacetime it is
described by the DeWitt-Brehme (DWB) equation containing the Ricci term
and a tail term. We show that for the motion of elementary particles in
vacuum metrics, the DWB equation can be reduced to the covariant form of
the LD equation, which we use here. Generically, the LD equation is
plagued by runaway solutions, so we discuss computational ways of
avoiding this problem when constructing numerical solutions. We also use
the first iteration of the covariant LD equation, which is the covariant
Landau-Lifshitz equation, comparing the results of these two approaches
and showing the smallness of the third-order Schott term in the
ultrarelativistic case. We calculate the corresponding energy and
angular momentum loss of a particle and study the damping of charged
particle oscillations around an equilibrium radius. We find that,
depending on the orientation of the Lorentz force, the oscillating
charged particle either spirals down to the black hole or stabilizes the
circular orbit by decaying its oscillations. The latter case leads to
the interesting new result of the particle orbit shifting outwards from
the black hole. We also discuss the astrophysical relevance of the
presented approach and provide estimates of the main parameters of the
model.
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Radiation reaction acting on a charged particle moving at a stable
circular orbit of a magnetized black hole (BH) can lead to the shift of
the orbital radius outward from the BH. The effect causes an increase of
the energy and angular momentum of the particle measured by an observer
at rest at infinity. In this paper, we show that "widening" of such
orbits is independent of the field configuration, but it appears only in
the cases with the external Lorentz force acting outward from the BH.
This condition corresponds to qLB > 0, where q and L are the charge
and angular momentum of the particle, and B is intensity of the external
magnetic field. As examples of the orbital widening, we consider two
scenarios with an external homogeneous magnetic field and a magnetic
dipole field generated by a current loop around a Schwarzschild BH. We
show that the orbital widening is accompanied by quasi-harmonic
oscillations of the particle, which are considerably large in the
magnetic dipole fields. We also estimate the timescales of orbital
widening, from which it follows that the effect can be relevant in the
vicinity of stellar-mass BHs.
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A test fluid composed of relativistic collisionless neutral particles in
the background of Kerr metric is expected to generate non-isotropic
equilibrium configurations in which the corresponding stress-energy
tensor exhibits pressure and temperature anisotropies. This arises as a
consequence of the constraints placed on single-particle dynamics by
Killing tensor symmetries, leading to a peculiar non-Maxwellian
functional form of the kinetic distribution function describing the
continuum system. Based on this outcome, in this paper the generation of
Kerr-like metric by collisionless N -body systems of neutral matter
orbiting in the field of a rotating black hole is reported. The result
is obtained in the framework of covariant kinetic theory by solving the
Einstein equations in terms of an analytical perturbative treatment
whereby the gravitational field is decomposed as a prescribed background
metric tensor described by the Kerr solution plus a self-field
correction. The latter one is generated by the uncharged fluid at
equilibrium and satisfies the linearized Einstein equations having the
non-isotropic stress-energy tensor as source term. It is shown that the
resulting self-metric is again of Kerr type, providing a mechanism of
magnification of the background metric tensor and its qualitative
features.
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Ringed accretion disks (RADs) are agglomerations of perfect-fluid tori
orbiting around a single central attractor that could arise during
complex matter inflows in active galactic nuclei. We focus our analysis
to axi-symmetric accretion tori orbiting in the equatorial plane of a
supermassive Kerr black hole; equilibrium configurations, possible
instabilities, and evolutionary sequences of RADs were discussed in our
previous works. In the present work we discuss special instabilities
related to open equipotential surfaces governing the material funnels
emerging at various regions of the RADs, being located between two or
more individual toroidal configurations of the agglomerate. These open
structures could be associated to proto-jets. Boundary limiting surfaces
are highlighted, connecting the emergency of the jet-like instabilities
with the black hole dimensionless spin. These instabilities are
observationally significant for active galactic nuclei, being related to
outflows of matter in jets emerging from more than one torus of RADs
orbiting around supermassive black holes.
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The electromagnetic (EM) perturbations of the black hole solutions in
general relativity coupled to nonlinear electrodynamics (NED) are
studied for both electrically and magnetically charged black holes,
assuming that the EM perturbations do not alter the spacetime geometry.
It is shown that the effective potentials of the electrically and
magnetically charged black holes related to test perturbative NED EM
fields are related to the effective metric governing the photon motion,
contrary to the effective potential of the linear electrodynamic
(Maxwell) field that is related to the spacetime metric. Consequently,
corresponding quasinormal (QN) frequencies differ as well. As a special
case, we study new family of the NED black hole solutions which tend in
the weak field limit to the Maxwell field, giving the Reissner-Nordström
(RN) black hole solution. We compare the NED Maxwellian black hole QN
spectra with the RN black hole QN spectra.
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We determine the class of axisymmetric and asymptotically flat black-
hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi
equations allow for the separation of variables. The known Kerr, Kerr-
Newman, Kerr-Sen and some other black-hole metrics in various theories
of gravity are within the class of spacetimes described here. It is
shown that although the black-hole metric in the Einstein-dilaton-Gauss-
Bonnet theory does not allow for the separation of variables (at least
in the considered coordinates), for a number of applications it can be
effectively approximated by a metric within the above class. This gives
us some hope that the class of spacetimes described here may be not only
generic for the known solutions allowing for the separation of
variables, but also a good approximation for a broader class of metrics,
which does not admit such separation. Finally, the generic form of the
axisymmetric metric is expanded in the radial direction in terms of the
continued fractions and the connection with other black-hole
parametrizations is discussed.
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We construct the light escape cones of isotropic spot sources of
radiation residing in special classes of reference frames in the Kerr-de
Sitter (KdS) black hole spacetimes, namely in the fundamental class of
`non-geodesic' locally non-rotating reference frames (LNRFs), and two
classes of `geodesic' frames, the radial geodesic frames (RGFs), both
falling and escaping, and the frames related to the circular geodesic
orbits (CGFs). We compare the cones constructed in a given position for
the LNRFs, RGFs, and CGFs. We have shown that the photons locally
counter-rotating relative to LNRFs with positive impact parameter and
negative covariant energy are confined to the ergosphere region.
Finally, we demonstrate that the light escaping cones govern the shadows
of black holes located in front of a radiating screen, as seen by the
observers in the considered frames. For shadows related to distant
static observers the LNRFs are relevant.
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