Perfect fluid tori with uniform distribution of the specific angular
momentum, l(r θ)= const, orbiting the Kerr-de Sitter naked
singularities are discussed. Closed equipotential surfaces
corresponding to stationary thick discs are allowed only in the
spacetimes admitting stable circular geodesics. The last closed surface
crosses itself in the cusp(s) enabling outflows of matter from the torus
due to the violation of hydrostatic equilibrium. The inner cusp enables
the accretion onto the ring singularity. Influence of the repulsive
cosmological constant, Λ > 0, resides in the existence of the
outer cusp enabling the excretion (outflow of matter from the torus into
the outer space) and gives rise to completely new type of a disc called
the excretion disc. The plus-family accretion and excretion discs can
be both the corotating or counterrotating discs, the minus-family ones
are always the counterrotating discs, as related to locally non-rotating
frames. If the parameters of naked-singularity spacetimes are very
close to the parameters of the extreme black-hole spacetimes, the family
of possible disc-like configurations includes members with two isolated
discs where the inner one is always a counterrotating accretion disc,
while the outer one can be the corotating or counterrotating excretion
disc, as well as the counterrotating accretion disc.
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Properties of the gravitational perturbation force caused by a small
inhomogeneity located on the surface of a neutron star are studied. The
oscillating perturbation force in both the accretion disc rotating
around the star and in the interior of a differentially rotating star is
determined. Both vertical and radial components of the force are given
and their relations are discussed. The frequency of the oscillations is
given by the difference of the frequency of the rotation of the star
surface, and the orbital frequency in the disc (the frequency of
rotation of matter in the star interior). Outside the star, in the disc,
the vertical and radial forces vary with the same phase. Inside a
differentially rotating star, the variations of the forces are in the
opposite phase in an internal part of the star, while they are in the
same phase in an external layer of the star. In an intermediate part of
the star, an additional oscillatory change appears. Is is shown that the
anharmonic character of the oscillatory forces is limited to the seventh
non-negligible harmonics. For completeness, we present the perturbation
force generated by a symmetric accretion column.
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The equation governing small radial oscillations and the related
Sturm-Liouville eigenvalue equation for eigenmodes of the oscillations
are determined for spherically symmetric configurations of perfect fluid
in spacetimes with a nonzero cosmological constant. The Sturm-Liouville
equation is then applied in the cases of spherically symmetric
configurations with uniform distribution of energy density and
polytropic spheres. It is shown that a repulsive cosmological constant
rises the critical adiabatic index and decreases the critical radius
under which the dynamical instability occurs.
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The Friedman models of the Universe with the superstring dark energy are
constructed. According to the spacetime foam approach the stringy dark
energy appears to be inversely proportional to the cosmic scale factor.
Evolution of the Friedman models is discussed under this assumption and
compared with the standard models.
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The Swiss cheese model of the Universe with the superstring dark energy
is constructed. The junction conditions are shown to be fulfilled and
time evolution of the matching hypersurface of the internal
Schwarzschild spacetime and homogeneous external Friedman Universe is
studied.
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Equilibrium conditions and spin dynamics of spinning test particles are
discussed in the stationary and axially symmetric Kerr-de Sitter
black-hole or naked-singularity spacetimes. The general equilibrium
conditions are established, but due to their great complexity, the
detailed discussion of the equilibrium conditions and spin dynamics is
presented only in the simple and most relevant case of equilibrium
positions in the equatorial plane of the spacetimes. It is shown that
due to the combined effect of the rotation of the source and the cosmic
repulsion the equilibrium is spin dependent in contrast to the
spherically symmetric spacetimes.
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It is highly probable that a non-linear resonance between some modes of
oscillations in the accretion discs around black holes and neutron stars
can play a crucial role in exciting detectable modulations of the X-ray
flux. Detailed studies of the resonance models revealed that several of
such non-linear resonances are possible in nearly Keplerian discs in
strong gravity. Moreover, this idea seems to be strongly supported by
observations - in all four microquasars showing twin peak QPOs
(quasiperiodic oscillations), the ratio of frequency peaks is 3:2. In
principle, using known frequencies of the twin peaks and the known mass
of the central black hole, the black-hole spin can be determined. This
was already done for the presently known sources and few miscellaneous
resonance models. Details of excitation mechanisms of eventual
resonances are still not fully explained, nevertheless one can imagine
that not only one resonance could be excited in the accretion disc.
Thus, if two such different resonances are present (by an accident or
because of some causal connection), the black hole spin can be precisely
determined independently of the knowledge of the black hole mass, for
some specific cases discussed here.
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Extremely compact objects (R<3 GM/c2) contain null
geodesics that are captured by the object. Certain part of neutrinos
produced in their interior will therefore be trapped, thus influencing
neutrino luminosity of the objects and their thermal evolution. This
effect was investigated for the interior Schwarzschild spacetimes with
the uniform distribution of energy density by Stuchlík, Z.,
Török, G., Hledík, S. and Urbanec, M. (2005), Neutrino
trapping in extremely compact objects, Classical Quantum Gravity,
submitted. We will investigate here influence of the cosmological
constant on the trapping phenomena. We use again the simplest model for
interior of such objects based on the interior Schwarzschild-(anti-)de
Sitter spacetimes. We determine behaviour of the trapping coefficients,
i.e., ``global'' one representing influence on the neutrino luminosity
and ``local'' one representing influence on the cooling process.
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Relativistic Keplerian orbital frequency (νK) and the
related epicyclic frequencies (radial νr, vertical
νθ) play an important role in the physics of
accretion discs orbiting Kerr black holes. We examine in detail their
properties in Kerr spacetimes and discuss some possible observational
implications resulting from their behaviour in the black hole case.
Characteristics of the fundamental orbital frequencies of Keplerian
motion are also analysed with the intention to find the phenomena which
could observationally distinguish a hypothetical naked singularity from
black holes. We explore the significant differences in behaviour of the
epicyclic frequencies. These suggest that oscillations of discs orbiting
Kerr black holes and naked singularities could be very different, and
the information, given through X-ray variability of the source, could
distinguish between the naked singularities and the black holes in
general.
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The discussion of the latitudinal and radial photon motion in the Kerr-
de Sitter (KdS) spacetime is examined by using the ``Chinese boxes''
technique. Only the case with a positive cosmological constant is
considered. The latitudinal motion is discussed by using a new motion
constant Q vanishing for motion in the equatorial plane. This will be
more comfortable for the next discussion of the photon off-equatorial
motion in KdS spacetime. For the radial motion an ``effective
potential'' governing the photon radial motion is used, circular photon
orbits are determined and their stability is discussed.
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