The role of a nonzero cosmological constant is discussed for black-hole
or naked-singularity spacetimes, Einstein-Strauss vacuola spacetimes,
and general relativistic polytropic fluid spheres. In case of the
black-hole spacetimes, motion of test particles and photons and
equilibrium configurations of test perfect fluid are considered. Their
relevance to astrophysically very important accretion processes in disk
regime is established.
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The role of a nonzero cosmological constant is discussed for black-hole or naked-singularity spacetimes, Einstein-Strauss vacuola spacetimes, and general relativistic polytropic fluid spheres. In case of the black-hole spacetimes, motion of test particles and photons and equilibrium configurations of test perfect fluid are considered. Their relevance to astrophysically very important accretion processes in disk regime is established.
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The influence of a repulsive cosmological constant on accretion
processes onto black holes is discussed. The steady, spherically
symmetric adiabatic inflow and outflow of perfect fluid is considered.
Further, the attention is focused on the properties of both
geometrically thin, Keplerian accretion disks and geometrically thick,
toroidal disks having relevant pressure gradients. It is shown that
nearby the static radius, where the gravitational attraction of a black
hole is just balanced by the cosmological repulsion, the accretion
toroidal disks have an outer cusp enabling outflow of matter from the
disk. Behind the static radius the cosmological repulsion efficiently
collimates jets that emanate along the rotation axis of the toroidal
disk.
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Recent developments in the field of relativistic astrophysics related to
accretion processes onto black holes and neutron stars, and to general
phenomena connected to the properties of black holes, and the internal
structure of neutron stars and quark stars, are discussed.
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The influence of a repulsive cosmological constant on accretion processes onto black holes is discussed. The steady, spherically symmetric adiabatic inflow and outflow of perfect fluid is considered. Further, the attention is focused on the properties of both geometrically thin, Keplerian accretion disks and geometrically thick, toroidal disks having relevant pressure gradients. It is shown that nearby the static radius, where the gravitational attraction of a black hole is just balanced by the cosmological repulsion, the accretion toroidal disks have an outer cusp enabling outflow of matter from the disk. Behind the static radius the cosmological repulsion efficiently collimates jets that emanate along the rotation axis of the toroidal disk.
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Recent developments in the field of relativistic astrophysics related to accretion processes onto black holes and neutron stars, and to general phenomena connected to the properties of black holes, and the internal structure of neutron stars and quark stars, are discussed.
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The equilibrium of a charged test particle with spin located in the
Reissner-Nordström background with a nonzero cosmological constant
is investigated. The stationary equilibrium conditions resulting from
the equations of motion and the equations of spin dynamics have to be
satisfied simultaneously. It is shown that equilibrium conditions are
independent of the spin of the test particle. For uncharged particles,
they are satisfied at the so-called static radius, where gravitational
attraction is exactly compensated for by cosmological repulsion. For
charged particles, there is a variety of possible equilibria due to the
electromagnetic interaction of the particle and the background. Any
charged particle can be in an unstable equilibrium state between the
black-hole and cosmological horizons of asymptotically de Sitter
spacetimes, while sufficiently repulsed particles can be in an inner
unstable equilibrium state and an outer stable equilibrium state above
the horizon of asymptotically anti-de Sitter spacetimes. The
separation-independent equilibrium is possible in extreme
Reissner-Nordström spacetimes only.
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The equilibrium of a charged test particle with spin located in the Reissner-Nordström background with a nonzero cosmological constant is investigated. The stationary equilibrium conditions resulting from the equations of motion and the equations of spin dynamics have to be satisfied simultaneously. It is shown that equilibrium conditions are independent of the spin of the test particle. For uncharged particles, they are satisfied at the so-called static radius, where gravitational attraction is exactly compensated for by cosmological repulsion. For charged particles, there is a variety of possible equilibria due to the electromagnetic interaction of the particle and the background. Any charged particle can be in an unstable equilibrium state between the black-hole and cosmological horizons of asymptotically de Sitter spacetimes, while sufficiently repulsed particles can be in an inner unstable equilibrium state and an outer stable equilibrium state above the horizon of asymptotically anti-de Sitter spacetimes. The separation-independent equilibrium is possible in extreme Reissner-Nordström spacetimes only.
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Null geodesics and embedding diagrams of central planes in the ordinary
space geometry and the optical reference geometry of the interior
Schwarzschild-de Sitter spacetimes with uniform density are studied. For
completeness, both positive and negative values of the cosmological
constant are considered. The null geodesics are restricted to the
central planes of these spacetimes, and their properties can be
reflected by an ``effective potential.'' If the interior spacetime is
extremely compact, the effective potential has a local maximum
corresponding to a stable circular null geodesic around which bound null
geodesics are concentrated. The upper limit on the size of the interior
spacetimes containing bound null geodesics is R=3M, independently of the
value of the cosmological constant. The embedding diagrams of the
central planes of the ordinary geometry into three-dimensional Euclidean
space are well defined for the complete interior of all spacetimes with
a repulsive cosmological constant, but the planes cannot be embedded
into the Euclidean space in the case of spacetimes with subcritical
values of an attractive cosmological constant. On the other hand, the
embedding diagrams of the optical geometry are well defined for all of
the spacetimes, and the turning points of these diagrams correspond to
the radii of the circular null geodesics. All the embedding diagrams,
for both the ordinary and optical geometry, are smoothly matched to the
corresponding embedding diagrams of the external vacuum Schwarzschild-de
Sitter spacetimes.
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Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild-de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an ``effective potential.'' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild-de Sitter spacetimes.
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