In all four microquasars which show twin peak kHz QPOs, the ratio of the
two frequencies is 3:2. This rather strongly supports the suggestion by
Abramowicz, M. A. and Kluzniak [W. Abramowicz, M. A. and Kluzniak, W.,
(2001). A precise determination of black hole spin in GRO J1655-40.
Astronomy and Astrophysics, 374:L19] that twin peak kHz QPOs are due to
a resonance between some modes of accretion disk oscillations. Detailed
studies of this suggestion revealed that several such non-linear
resonances are present in nearly Keplerian disks in strong gravity.
Here, we fit to observations predictions of the resonance hypothesis for
two particular types of non-linear resonances between vertical and
radial epicyclic frequencies. For three microquasars with known masses,
the fits give an accurate estimate of the spin.
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Solutions of general relativistic field equations for static,
spherically symmetric, equilibrium perfect-fluid configurations obeying
the polytropic and adiabatic equation of state in the presence of a
repulsive cosmological constant are discussed. The influence of the
cosmological constant on the total mass of the configurations, their
radius and the profiles of energy density, rest energy density, pressure
and metric coefficients is studied and compared for the polytropic and
adiabatic case. The static equilibrium configurations are allowed for
σ<σ_{crit} (α<α_{crit}), where the
critical values σ_{crit} (α_{crit}) of the relativity
parameter σ (α) ≡ pcent/rhocent c^{2} of the
polytropes (adiabates) depend on the cosmological constant and the
polytropic index n of the equation of state and can be determined by a
numerical procedure. The numerical results show that for sufficiently
small values of the relativity parameter σ=α≪
σ_{crit}, the polytropic spheres are more compact than the
adiabatic ones. Increase of the cosmological constant causes increase of
both the radius and mass of the spheres and makes the profiles of the
metric coefficients flatter. For large values of the relativity
paramater, σ=α≲ σ_{crit}, the situation is more
complex and depends also on the value of the polytropic parameter n. The
mass of the adiabatic spheres can exceed the mass of the polytropes for
n≳ 2. In the case of n=3, the adiabatic spheres can even be more
compact than the polytropic ones. Generally, the role of the
cosmological constant is supressed with both σ=α and n
growing.
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Definition of the inertial forces in the framework of the optical
reference geometry is applied to the stationary and axially symmmetric
Kerr-de Sitter spacetimes. The attention is restricted to the inertial
forces acting on particles moving along circular orbits in the
equatorial plane of these spacetimes. It is shown, where the
gravitational force vanishes, and where the centrifugal force vanishes
independently of velocities of test particles. The Coriolis force does
not vanish for a non-zero velocity.
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We consider appearance of isotropically radiating sources located at a
sphere at the static radius of the Schwarzschild-de Sitter spacetimes to
static observers in vicinity of the black hole horizon and the
cosmological horizon and to radially moving observers. We expect these
observers to follow geodesics starting from the static radius. It is
shown that the observed flux diverges at both the horizons for both
classes of observers. Nevertheless the frequency shift remains finite at
the horizons for the radially moving observers.
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The role of the observed relict vacuum energy on the fluctuations of
CMBR going through cosmological matter condensations is studied in the
framework of the Einstein-Strauss-de Sitter vakuola model. It is shown
that refraction of light at the matching surface of the vakuola and the
expanding Friedman universe can be very important during the accelerated
expansion of the universe when the velocity of the matching surface
relative to static Schwarzschildian observers becomes relativistic.
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We consider basic properties of both the geometrically thin and thick
accretion disks in the Kerr-de Sitter black-hole and naked-singularity
spacetimes. The properties are determined by character of the equatorial
circular geodesics of these spacetimes and by the equilibrium
configurations of a perfect fluid rotating around their symmetry axis.
Transformation of a Kerr-de Sitter naked singularity into an extreme
black hole due to accretion in the thin disks is briefly discussed for
both the plus-family and minus-family disks. It is shown that such a
conversion leads to an abrupt instability of the innermost parts of the
plus-family accretion disks that can have strong observational
consequences.
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Aschenbach [Aschenbach, B. (2004). Measuring mass and angular momentum
of black holes with high-frequency quasi-periodic oscillations.
Astronomy and Astrophysics, 425:1075-1082] has shown that in Kerr
black-hole spacetimes with rotation parameter a>0.9953, the Keplerian
orbital velocity measured in locally non-rotating frames (LNRF) has a
positive radial gradient in a small region in the vicinity of the event
horizon and proposed that excitation of oscillations in Keplerian thin
discs can be related to this fact. Similarly, we show that in the
equatorial plane of marginally stable thick discs (with uniformly
distributed specific angular momentum ℓ(r,θ)=const) the
orbital velocity relative to the LNRF has a positive radial gradient in
the vicinity of black holes with a>0.99979. The change of sign of the
velocity gradient occurs just above the centre of the thick toroidal
discs, in the region where stable circular geodesics of the Kerr
spacetime are allowed. Therefore, the same mechanism as in the Keplerian
discs could trigger oscillations in thick discs, but the rotational
parameter of the Kerr spacetime must be much closer to the extreme-hole
state with a=1. The global character of the phenomenon is given in
terms of topology changes of the von Zeipel surfaces (equivalent to
equivelocity surfaces in the tori with ℓ (r,θ)=const).
Toroidal von Zeipel surfaces exist around the circle corresponding to
the minimum of the equatorial LNRF velocity profile, indicating a
possibility of development of some vertical instabilities in those parts
of marginally stable tori with positive gradient of the LNRF velocity.
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Extremely compact objects (9GM/4c^2<R<3GM/c^2) contain trapped
null geodesics that cannot escape the objects. Certain part of neutrinos
produced in their interior will therefore be trapped, thus influencing
neutrino luminosity of the objects and consequently their thermal
evolution. The existence of trapped neutrinos also indicates
possibility of ``two-temperature'' cooling regime of extremely compact
objects. It is shown that the trapping of neutrinos can be relevant
even for moderately extremely compact stars.
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Equatorial motion of test particles in Kerr de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both black-hole and naked-singularity spacetimes, and their relevance for thin accretion disks is established. The circular orbits constitute two families that coalesce at the so-called static radius. The orientation of the motion along the circular orbits is, in accordance with case of asymptotically flat Kerr spacetimes, defined by relating the motion to the locally nonrotating frames. The minus-family orbits are all counterrotating, while the plus-family orbits are usually corotating relative to these frames. However, the plus-family orbits become counterrotating in the vicinity of the static radius in all Kerr de Sitter spacetimes, and they become counterrotating in the vicinity of the ring singularity in Kerr de Sitter naked-singularity spacetimes with a low enough rotational parameter. In such spacetimes, the efficiency of the conversion of the rest energy into heat energy in the geometrically thin plus-family accretion disks can reach extremely high values exceeding the efficiency of the annihilation process. The transformation of a Kerr de Sitter naked singularity into an extreme black hole due to accretion in the thin disks is briefly discussed for both the plus-family and minus-family disks. It is shown that such a conversion leads to an abrupt instability of the innermost parts of the plus-family accretion disks that can have strong observational consequences.
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Equatorial motion of test particles in Kerr de Sitter spacetimes is
considered. Circular orbits are determined, their properties are
discussed for both black-hole and naked-singularity spacetimes, and
their relevance for thin accretion disks is established. The circular
orbits constitute two families that coalesce at the so-called static
radius. The orientation of the motion along the circular orbits is, in
accordance with case of asymptotically flat Kerr spacetimes, defined by
relating the motion to the locally nonrotating frames. The minus-family
orbits are all counterrotating, while the plus-family orbits are usually
corotating relative to these frames. However, the plus-family orbits
become counterrotating in the vicinity of the static radius in all Kerr
de Sitter spacetimes, and they become counterrotating in the vicinity of
the ring singularity in Kerr de Sitter naked-singularity spacetimes with
a low enough rotational parameter. In such spacetimes, the efficiency of
the conversion of the rest energy into heat energy in the geometrically
thin plus-family accretion disks can reach extremely high values
exceeding the efficiency of the annihilation process. The transformation
of a Kerr de Sitter naked singularity into an extreme black hole due to
accretion in the thin disks is briefly discussed for both the
plus-family and minus-family disks. It is shown that such a conversion
leads to an abrupt instability of the innermost parts of the plus-family
accretion disks that can have strong observational consequences.
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