The possibility of equilibrium of test particles with spin located in
the Schwarzschild - de Sitter spacetimes 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 the equilibrium conditions are independent of the spin of the
test particles; they are satisfied only at the so called static radius
where the gravitational attraction is compensated by the cosmological
repulsion.
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The possibility of equilibrium of test particles with spin located in the Schwarzschild - de Sitter spacetimes 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 the equilibrium conditions are independent of the spin of the test particles; they are satisfied only at the so called static radius where the gravitational attraction is compensated by the cosmological repulsion.
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The differences between the character of the Schwarzschild and Ernst
spacetimes are illustrated by comparing the photon capture cones, and
the embedding diagrams of the 0264-9381/16/4/026/img1 sections of the
equatorial planes of both the ordinary and optical reference geometry of
these spacetimes. The non-flat asymptotic character of the Ernst
spacetime reflects itself in two manifest facts: the escape photon cones
correspond to a purely outward radial direction, and the embedding
diagrams of both the ordinary and optical geometry shrink to zero radius
asymptotically. Using the properties of the embedding diagrams, regions
of these spacetimes which could have similar character are estimated,
and it is argued that they can exist for the Ernst spacetimes with a
sufficiently low strength of the magnetic field.
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The differences between the character of the Schwarzschild and Ernst spacetimes are illustrated by comparing the photon capture cones, and the embedding diagrams of the 0264-9381/16/4/026/img1 sections of the equatorial planes of both the ordinary and optical reference geometry of these spacetimes. The non-flat asymptotic character of the Ernst spacetime reflects itself in two manifest facts: the escape photon cones correspond to a purely outward radial direction, and the embedding diagrams of both the ordinary and optical geometry shrink to zero radius asymptotically. Using the properties of the embedding diagrams, regions of these spacetimes which could have similar character are estimated, and it is argued that they can exist for the Ernst spacetimes with a sufficiently low strength of the magnetic field.
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A restricted repulsive barrier exists for equatorial photon motion in
some Kerr-Newman-de Sitter black-hole spacetimes, due to an interplay
between the rotation of the source and the cosmological repulsion. Quite
surprisingly, photons with high positive and all negative values of
their impact parameter can travel freely between the black-hole horizon
and the cosmological horizon in these spacetimes. The special class of
the Kerr-Newman-de Sitter spacetimes with restricted repulsive barriers
is represented in the space of the parameters of the geometry. The area
of the parameter space corresponding to this class is largest in the
case of Kerr-de Sitter spacetimes. With the charge parameter of the
spacetime growing, the area shrinks. In all of these cases, the mass
parameter of the spacetime must be so high that the sizes of the
black-hole and cosmological horizons are comparable.
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