Using known frequencies of the accretion disc twin peak quasiperiodic
oscillations (QPOs) and the known mass of the central black hole, the
black hole dimensionless spin a can be determined, assuming a concrete
version of the orbital resonance model. However, because of large range
of observationally limited values of the black hole mass, its spin can
be estimated with a low precision only. Higher precision of the black
hole spin measurement is possible in the framework of multi-resonance
model of QPOs inspired by complex high-frequency QPO patterns observed
in some black hole and neutron star systems. In the simple orbital
resonance models we determine the spin and mass dependence of the twin
peak frequencies for non-linear resonances of oscillations with the
epicyclic and Keplerian frequencies or their combinations in the case of
a general rational frequency ratio n : m, n > m. In the
multi-resonant model, the twin peak resonances are combined properly to
give the observed frequency set. The multi-resonant model is proposed in
three distinct versions. In the first one, related probably to the
neutron star binary systems, more instances of one resonance occur at
more specific radii. In the second case, more resonances are sharing one
specific radius, allowing for "cooperative" resonant phenomena in the
field of black holes with a specific value of spin. In the third
("ugly") case, more resonances occur at more specific radii; we restrict
our attention to the case of two such resonant radii. For special values
of the spin, only triple-set of frequencies is observed because of
coincidence of some frequencies, allowing determination of the spin from
the triple frequency ratio set. The spin is determined precisely, but
not uniquely as the same frequency set could be relevant for more than
one concrete spin and combination of resonant oscillations.
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Rotating black holes in the brany universe of the Randall-Sundrum type
with infinite additional dimension are described by the Kerr geometry
with a tidal charge b representing the interaction of the brany black
hole and the bulk spacetime. We investigate the role of the tidal charge
in the orbital resonance model of quasiperiodic oscillations (QPOs) in
black hole systems. The orbital Keplerian frequency ν_{K} and the
radial and vertical epicyclic frequencies ν_{r}, ν_{θ} of
the equatorial, quasicircular geodetical motion are discussed, and the
local maxima of their radial profiles related to Keplerian accretion
discs are given, assuming the inner edge of the disc located at loci of
the innermost stable circular geodesic. The resonant conditions are
given for possible direct (parametric) resonances of the oscillations
with the radial and vertical epicyclic frequencies and for some trapped
oscillations of the warped discs with resonant combinational frequencies
involving the Keplerian and radial epicyclic frequencies. It is shown,
how the tidal charge could influence matching of the observational data
indicating the 3:2 frequency ratio observed in GRS 1915+105 microquasar
with prediction of the orbital resonance model. The "magic"
dimensionless black hole spin enabling presence of strong resonant
phenomena at the radius, where ν_{K}:ν_{θ}:ν_{r} =
3:2:1, is determined in dependence on the tidal charge. Such strong
resonances could be relevant even in sources with highly scattered
resonant frequencies, as those expected in Sgr A*.
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High-frequency QPOs in neutron-star binary systems could be explained by
models based on parametric or forced resonance between oscillation modes
of the accretion disc around the neutron star (with frequencies related
to the Keplerian and epicyclic frequencies of the disc) and the relative
rotational motion between the disc material and either the neutron star
or the binary companion.
Using Newtonian theory, we discuss the possibility of forced resonant
phenomena being excited by means of gravitational perturbations coming
from surface features on the neutron star and from the companion star.
For each potential perturbation source, we have determined the Fourier
decomposition of the gravitational perturbing forces acting on disc
elements in the radial and vertical directions. The analysis presented
for the binary companion can be applied also to black hole systems but
the surface features would not be present in that case.
The oscillations induced by the binary partner are of a different
character from those which would be induced by a mountain or by the
accretion columns. In the case of symmetric accretion columns, the
excitation frequency in the radial direction is twice that in the
vertical direction and higher order modes could be relevant for parts of
the disc very close to the neutron star. In this inner region, the
influence of the accretion columns is greater than that of the binary
companion for producing forced oscillations in both the radial and
vertical directions; in the intermediate part, the vertical oscillations
are induced by the accretion columns while the radial oscillations are
excited by the binary partner (if appropriate conditions are fulfilled);
sufficiently far from the neutron star, the binary companion has the
greater effect. The limits on the magnitude of neutron star deformations
given by the possibility to excite observable QPOs coincide with
restrictions coming from (non-)observations of gravitational waves by
LIGO.
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Trapping of neutrinos in brany extremely compact stars is studied, using
the simplest model with massless neutrinos and uniform-density star. The
influence of bulk tension on the trapping is given for two solutions,
namely with the Reissner-Nordström-type of geometry described by a
single brany parameter, and the second one determined by the energy
density of the star and the brane tension.
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Humpy radial profiles of the LNRF-related orbital velocity was found for
a circular motion of test particles and test perfect fluid orbiting
near-extreme Kerr black holes and Kerr naked singularities. Preliminary
results of an analogical study of the circular motion of test particles
and fluid in the Kerr-(anti-)de Sitter spacetimes are presented.
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The "Extended Orbital Resonance Model", i.e., the idea of oscillations
induced by the hump of the orbital velocity profile (related to the
locally non-rotating frames - LNRF), which are proposed to excite the
oscillations of Keplerian discs around near-extreme Kerr black holes
with epicyclic frequencies, is used to estimate the mass and spin of
three near-extreme Kerr black hole candidates GRS 1915+105, XTE
J1650-500, and NGC 5408 X-1. The hump-induced oscillations are
characterized by the so-called "humpy frequency", and a non-linear
resonant coupling between these and epicyclic oscillations is expected.
It it shown that the quasiperiodic variability (QPOs) observed in these
sources can be matched with the proposals of the model, giving for the
mass and spin of their black holes values consistent with the other
observationally-established estimates.
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In the framework of the brany models, rotating black holes are described
by the Kerr metric with a tidal charge representing the influence of the
shear effects of the bulk space Weyl tensor onto the black hole
spacetime. Here we study the influence of the tidal charge onto some
optical phenomena in rotating black hole spacetimes. The photon motion
is given in terms of constants of the geodetical motion related to the
spacetime symmetries and escape photon cones are given for special
families of locally non-rotating, circular geodetical and radially
freely-falling observers. The shadow of a rotating black hole and the
shape of an equatorial thin accretion disk are given and classified in
terms of the black hole rotational and tidal parameters.
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In the framework of the brany models, rotating black holes are described
by the Kerr metric with a tidal charge representing the influence of the
non-local gravitational (tidal) effects of the bulk space Weyl tensor
onto the black hole spacetime. Here we study the influence of the tidal
charge onto profiled spectral lines generated by radiating tori orbiting
in vicinity of a rotating black hole. We show that with lowering the
negative tidal charge of the black hole, the profiled line becomes to be
flatter and wider.
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Being inspired by existence of non-equatorial circular (halo) stable
orbits of charged particles in composite of gravitational, dipole
magnetic and co-rotational electric fields near some planets, we find
possible existence of these orbits in strong gravitational fields
described by the Kerr-Newman geometry. By using the general relativistic
inertial forces formalism combined with the effective potential
approach, we show that the stable halo orbits do exist there. But it
seems that they are out of the astrophysical importance, being hidden
under the inner black-hole horizon, or appearing in the naked
singularity spacetimes.
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In the framework of the brany cosmology, the influence of the bulk
spacetime on the black holes in the brane can be described by the so
called tidal charge, which has a character similar to the charge
parameter in the standard black-hole solutions, but can be both positive
and negative. We discuss the influence of the tidal charge on the test
particle and photon motion in the spherically symmetric spacetimes with
a nonzero cosmological constant using the analysis realised in the case
of Reissner-Nordström-(anti-)de Sitter spacetimes. We concentrate
on the properties of circular geodesics as they play an important role
in determining the brane properties of both thin and thick accretion
discs. Some implications of the tidal charge influence are outlined.
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