The external Hartle─Thorne geometry, which describes the spacetime
outside a slowly rotating compact star, is characterized by the
gravitational mass M, angular momentum J, and quadrupole moment Q of the
star and gives a convenient description, which, for the rotation
frequencies of more than 95% of known pulsars, is sufficiently accurate
for most purposes. We focus here on the motion of particles in these
spacetimes, presenting a detailed systematic analysis of the frequency
properties of radial and vertical epicyclic motion and of orbital
motion. Our investigation is motivated by X-ray observations of binary
systems containing a rotating neutron star that is accreting matter from
its binary companion. In these systems, twin high-frequency quasi-
periodic oscillations (QPOs) are sometimes observed with a frequency
ratio approaching 3:2 or 5:4, and these may be explained by models
involving the orbital and epicyclic frequencies of quasi-circular
geodesic motion. In our analysis, we use realistic equations of state
for the stellar matter and proceed in a self-consistent way, following
the Hartle─Thorne approach in calculating both the corresponding values
of Q, M, and J for the stellar model and the properties of the
surrounding spacetime. Our results are then applied to a range of
geodetical models for QPOs. A key feature of our study is that it
implements the recently discovered universal relations among neutron-
star parameters so that the results can be directly used for models with
different masses M, radii R, and rotational frequencies f
_{rot}.
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Using the gravitational decoupling by the minimal geometric deformation
approach, we build an anisotropic version of the well-known Tolman VII
solution, determining an exact and physically acceptable interior two-
fluid solution that can represent behavior of compact objects.
Comparison of the effective density and density of the perfect fluid is
demonstrated explicitly. We show that the radial and tangential pressure
are different in magnitude giving thus the anisotropy of the modified
Tolman VII solution. The dependence of the anisotropy on the coupling
constant is also shown.
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We study behaviour of ionized region of a Keplerian disk orbiting a
Schwarzschild black hole immersed in an asymptotically uniform magnetic
field. In dependence on the magnetic parameter B, and inclination angle
θ of the disk plane with respect to the magnetic field direction, the
charged particles of the ionized disk can enter three regimes: (1)
regular oscillatory motion, (2) destruction due to capture by the
magnetized black hole, (3) chaotic regime of the motion. In order to
study transition between the regular and chaotic type of the charged
particle motion, we generate time series of the solution of equations of
motion under various conditions, and study them by non-linear (box
counting, correlation dimension, Lyapunov exponent, recurrence analysis,
machine learning) methods of chaos determination. We demonstrate that
the machine learning method appears to be the most efficient in
determining the chaotic region of the θ -r space. We show that the
chaotic character of the ionized particle motion increases with the
inclination angle. For the inclination angles θ ̃ 0 whole the ionized
internal part of the Keplerian disk is captured by the black hole.
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We employ the minimal geometric deformation approach to gravitational
decoupling (MGD-decoupling) in order to build an exact anisotropic
version of the Schwarzschild interior solution in a space-time with
cosmological constant. Contrary to the well-known Schwarzschild
interior, the matter density in the new solution is not uniform and
possesses subluminal sound speed. It therefore satisfies all standard
physical requirements for a candidate astrophysical object.
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Classical (quasinormal) and quantum (Hawking) radiations are
investigated for test fields in the background of a four dimensional,
spherically symmetric and asymptotically flat black hole in the
Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB
black hole deviates from the Schwarzschild geometry only slightly.
Therefore, here we observe that the quasinormal spectrum also deviates
from its Schwarzschild limit at most moderately, allowing for a 9%
decrease in the damping rate and up to a 6% decrease in the real
oscillation frequency. However, the intensity of Hawking radiation of an
electromagnetic and Dirac fields turned out to be much more sensitive
characteristic than its quasinormal spectrum, allowing for a 57% and 48%
increase of the energy emission rate respectively. The analytical
formula for the eikonal regime of quasinormal modes is derived for test
fields and it is shown that the correspondence between the eikonal
quasinormal modes and null geodesics is indeed fulfilled for test
fields, but is not expected for the gravitational one.
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The Schwarzschild star is an ultracompact object beyond the Buchdahl
limit, which has Schwarzschild geometry outside its surface and positive
pressure in the external layer which vanishes at the surface. Recently
it has been shown that the Schwarzschild star is stable against
spherically-symmetric perturbations. Here we study arbitrary axial non-
spherical perturbations, and show that the observable quasinormal modes
can be as close to the Schwarzschild limit as one wishes, what makes the
Schwarzschild star a very good mimicker of a black hole. The decaying
time-domain profiles prove that the Schwarzschild star is stable against
non-spherical perturbations as well. Another peculiar feature is the
absence of echoes at the end of the ringdown. Instead we observe a non-
oscillating mode which might belong to the class of algebraically
special modes. At asymptotically late times, Schwarzschildian power-law
tails dominate in the signal.
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We employ the minimal geometric deformation approach to gravitational
decoupling (MGD-decoupling) in order to generate an exact anisotropic
and non-uniform version of the ultracompact Schwarzschild star, or
'gravastar', proposed by Mazur and Mottola. This new system represents
an ultracompact configuration of radius $R_{S}=2cal{M}$ whose interior
metric can be matched smoothly to a conformally deformed Schwarzschild
exterior. Remarkably, the model satisfies some of the basic requirements
to describe a stable stellar model, such as a positive density
everywhere and decreasing monotonously from the centre, as well as a
non-uniform and monotonic pressure.
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We study the optical properties of the Kehagias-Sfetsos (KS) compact
objects, characterized by the "Hov{r}ava" parameter $omega_{_{KS}}$,
in the presence of plasma, considering its homogeneous or power-law
density distribution. The strong effects of both "Hov{r}ava" parameter
$omega_{_{KS}}$ and plasma on the shadow cast by the KS compact objects
are demonstrated. Using the weak field approximation, we investigate the
gravitational lensing effect. Strong dependence of the deflection angle
of the light on both the "Hov{r}ava" and plasma parameter is explicitly
shown. The magnification of image source due to the weak gravitational
lensing is given for both the homogeneous and inhomogeneous plasma.
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We provide constraints on possible configurations and interactions of
two coplanar tori orbiting a central Kerr black hole (BH), in dependence
on its dimensionless spin. The two-tori configurations can be directly
linked to the current models featuring the obscuration of galactic BH
X-ray emission. The emergence of each torus instability phases is
discussed and tori collision has been also investigated. The first
simple evaluation of the center-of-mass energy proves that collision-
energy-efficiency increases with the dimensionless BH spin. We explore
the phenomenological aspects of the corotating and counterrotating tori
by analyzing properties of the orbiting toroidal configurations related
to the fluid enthalpy flux, the mass-flux, the mass-accretion-rates, and
the cusp luminosity in the two cases of corotating and counterrotating
fluids in dependence on the SMBH spin. The analysis resulted ultimately
in a comparative investigation of the properties of corotating versus
counterrotating tori, demonstrating that two accretion tori can orbit
around the central Kerr attractor only under very specific conditions.
Our results also demonstrate that the dynamics of the unstable phases of
these double tori systems is significant for the high energy phenomena
which could be observable in the X-ray emission and extremely energetic
phenomena in active galactic nuclei and quasar.
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We study the appearance of Keplerian accretion disks in order to
demonstrate the influence of the nonlinear electrodynamics (NED) on the
gravitational lensing and frequency shifting of the images of the
Keplerian disks. We focus our attention on the Bardeen black hole
backgrounds with magnetic charges that could be considered to be
acceptable solutions for the Einstein gravitational equations combined
with those representing an NED. Photons governing the appearance of the
Keplerian disks follow null geodesics of the effective geometry related
to the Bardeen spacetime. We compare the appearance governed by the
effective geometry to those governed by the spacetime geometry itself,
and to the appearance of Keplerian disks orbiting a related Reissner-
Nordstrom black hole spacetime. We demonstrate a clear and very strong
difference between the disk images determined by the effective geometry
and the others, both in the shape and (especially) in the frequency
mapping where it exhibits a difference of three orders.
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