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. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. 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 v K and the radial and vertical epicyclic frequencies v r, v θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, 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; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v K: v θ : v 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*. The specific values of the spin and tidal charge are given also for existence of specific radius where v K : v θ : v r = s : t : u with 5≥ s > t > u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.
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We present results of investigation of the off-equatorial circular
orbits existence in the vicinity of neutron stars, Schwarzschild black
holes with plasma ring, and near Kerr-Newman black holes and naked
singularities.
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We present results of investigation of the off-equatorial circular orbits existence in the vicinity of neutron stars, Schwarzschild black holes with plasma ring, and near Kerr-Newman black holes and naked singularities.
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Extremely compact objects (9GM/4c2 < R <
3GM/c2) contain trapped null geodesics. When such objects
enter the evolution period corresponding to the geodetical motion of
neutrinos, a certain part of neutrinos produced in their interior will
be trapped influencing thus neutrino luminosity of the objects and
consequently their thermal evolution. The existence of trapped neutrinos
indicates possibility of 'two-temperature' cooling regime of the
extremely compact objects. We present upper estimates on the efficiency
of the neutrino trapping effects obtained in the framework of the
simplest model of the internal Schwarzschild spacetime with uniform
distribution of energy density, assuming uniform distribution of
neutrino emissivity. We introduce a 'global' luminosity trapping
coefficient representing influence of the trapping effect on the total
neutrino luminosity of the extremely compact objects and cooling
trapping coefficients of both 'local' and 'global' kinds characterizing
influence of the trapping on the cooling process. It is shown that the
trapping of neutrinos can be relevant to moderately or even slightly
extremely compact objects.
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Extremely compact objects (9GM/4c2 < R < 3GM/c2) contain trapped null geodesics. When such objects enter the evolution period corresponding to the geodetical motion of neutrinos, a certain part of neutrinos produced in their interior will be trapped influencing thus neutrino luminosity of the objects and consequently their thermal evolution. The existence of trapped neutrinos indicates possibility of 'two-temperature' cooling regime of the extremely compact objects. We present upper estimates on the efficiency of the neutrino trapping effects obtained in the framework of the simplest model of the internal Schwarzschild spacetime with uniform distribution of energy density, assuming uniform distribution of neutrino emissivity. We introduce a 'global' luminosity trapping coefficient representing influence of the trapping effect on the total neutrino luminosity of the extremely compact objects and cooling trapping coefficients of both 'local' and 'global' kinds characterizing influence of the trapping on the cooling process. It is shown that the trapping of neutrinos can be relevant to moderately or even slightly extremely compact objects.
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We study the influence of the tidal charge parameter of the braneworld models on some optical phenomena in rotating black hole space-times. The escape photon cones are determined for special families of locally nonrotating, circular geodetical and radially free-falling observers. The silhouette of a rotating black hole, the shape of an equatorial thin accretion disk and the time delay effect for direct and indirect images of a radiating hot spot orbiting the black hole are given and classified in terms of the black hole rotational and tidal parameters. It is shown that increase of the negatively valued tidal parameter, with the rotational parameter fixed, generally strengthens the relativistic effects and suppresses the rotation-induced asymmetries in the optical phenomena.
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Results of our recent studies concerning possible effects of Λ > 0 for equilibrium positions of spinning test particles and stationary configurations of perfect-fluid tori are presented.
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We present results of our recent studies concerning effects of Λ > 0 in astrophysically motivated problems. Here we summarize properties of circular geodesic motion of test particles in the equatorial plane of Kerr-de Sitter black-hole and naked-singularity spacetimes. Along with the standard analysis of geodesic equations of the ordinary geometry, we introduce alternative inertial forces formalism defined within the General Theory of Relativity in the framework of optical reference geometry.
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High-frequency twin peak quasiperiodic oscillations (QPOs) are observed
in four microquasars, i.e., Galactic black hole binary systems, with
frequency ratio very close to 3:2. In the microquasar GRS 1915+105 the
structure of QPOs exhibits additional frequencies and more than two
frequencies are observed in the Galaxy nuclei Sgr A* or in some
extragalactic sources (NGC 4051, MCG-6-30-15 and NGC 5408 X-1). The
observed QPOs can be explained by a variety of the orbital resonance
model versions assuming resonance of oscillations with the Keplerian
frequency νK or the vertical epicyclic frequency
νθ, and the radial epicyclic frequency
νr, or some combinations of these frequencies. Generally,
different resonances could arise at different radii of an accretion
disk. However, we have shown that for special values of dimensionless
black hole spin a strong resonant phenomena could occur when different
resonances can be excited at the same radius, as cooperative phenomena
between the resonances may work in such situations. The special values
of a are determined for triple frequency ratio sets
νK:νθ:νr=s:t:u with
s,t,u being small integers. The most promising example of such a special
situation arises for black holes with extraordinary resonant spin
a=0.983 at the radius r=2.395 M, where
νK:νθ:νr=3:2:1. We also
predict that when combinations of the orbital frequencies are allowed,
QPOs with four frequency ratio set 4:3:2:1 could be observed in the
field of black holes with a=0.866,0.882 and 0.962. Assuming the
extraordinary resonant spin a=0.983 in Sgr A*, its QPOs with observed
frequency ratio ≍3:2:1 imply the black hole mass in the interval
4.3×106 Msolar< M<
5.4×106 Msolar, in agreement with estimates
given by other, independent, observations.
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Context: XTE J1650-500 is a Galactic black-hole binary system for which
at least one high-frequency QPO at 250 Hz has been reported. Moreover
there are indications that the system harbours a near-extreme Kerr black
hole with a spin aast ≃ 0.998 and mass M_BH ≲ 7.3
Msun. Recently it was discovered that the orbital 3-velocity
of test-particle (geodesical) discs orbiting Kerr black holes with a
spin aast > 0.9953, analyzed in the locally non-rotating
frames, reveals a hump near the marginally stable orbit. It was
suggested that the hump could excite the epicyclic motion of particles
near the ISCO with frequencies typical for high-frequency QPOs. The
characteristic frequency of the hump-induced oscillations was defined as
the maximal positive rate of change of the LNRF-related orbital velocity
with the proper radial distance. If the characteristic “humpy
frequency” and the radial epicyclic frequency are commensurable,
strong resonant phenomena are expected. Aims: We apply the idea
of hump-induced oscillations in accretion discs around near-extreme Kerr
black holes to estimate the black-hole mass in the XTE J1650-500 binary
system. Methods: For the Kerr black hole with spin
aast ≃ 0.9982 the characteristic “humpy
frequency” and the radial epicyclic frequency are in the ratio 1:3
at the orbit where the positive rate of change of the LNRF-related
orbital velocity with the proper radial distance is maximal. Identifying
the radial epicyclic frequency with the observed 250 Hz QPO, we arrive
at the mass of the black hole. In this method the ratio of frequencies
determines the spin (and vice versa), and the values of the frequencies
determine the black-hole mass. Results: The mass of the Kerr
black hole in XTE J1650-500 binary system is estimated to be around 5.1
Msun.
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