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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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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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 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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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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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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We examine halo orbits of electrically charged particles near a
magnetized compact star. We compare the Newtonian and Pseudo-Newtonian
approaches to the Störmer problem as a preliminary discussion of
the full general relativistic approach. We show the differences in the
effective potential that arise due to strong gravity near a gravitating
body.
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The integrals of photon motion in the Kerr spacetimes are given in terms
of the emission angles related to emitters moving along the circular
geodesic orbits. The local frames of the circular geodesic emitters are
given in relation to the locally nonrotating frames and local
directional angles of the escape cones are given in terms of the motion
constants of photons.
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Equilibrium configurations that are solutions of spherically symmetric
hydrostatic equations of General Relativity for an ideal fluid obeying a
polytropic (or adiabatic) equation of state are given in the framework
of general relativity. The equilibrium configurations are given in
terms of the polytropic index n and the so called relativistic parameter
σ (for polytropes) or α (for adiabates).
First, simple models of polytropic and adiabatic spheres for
non-relativistic and ultra-relativistic case of the equation of state
are introduced. Then, the comparison of polytropic and adiabatic spheres
is given in some special characteristic cases and the influence of the
relativistic parameter on the structure of the spheres and the
gravitational and binding energy.
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Embedding diagrams of the equatorial plane of the Kerr-de Sitter
black-hole or naked-singularity spacetimes are constructed for the
optical reference geometry. The embedding diagrams do not cover whole
stationary parts of the Kerr-de Sitter spacetimes. Hence, limits of
embeddability are discussed. The Kerr-de Sitter spacetimes are then
classified according to the number of embeddable regions and the number
of the turning points of the diagrams.
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