Properties of the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes are characterized by three phenomena, namely, by the ``effective potential'' of the motion of test particles and photons, the photon escape cones, and the embedding diagrams of t=const sections of central planes of both the ordinary and optical reference geometry of these spacetimes. The phenomena are related to the corresponding phenomena of the Schwarzschild spacetime, and differences caused by the asymptotic structure of the spacetimes with a nonzero cosmological constant are discussed. The properties of the embedding diagrams of the optical geometry are related to the dynamical behavior of test particles. The limits of the embeddability of the optical geometry are given and compared with the limits on the outer radius of the interior solutions of Einstein's equations with a nonzero cosmological constant for static, spherically symmetric configurations of uniform density. It is shown that, contrary to the pure Schwarzschild case, these limits do not fully coincide for repulsive cosmological constants.
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Properties of the Schwarzschild-de Sitter and Schwarzschild-anti-de
Sitter spacetimes are characterized by three phenomena, namely, by the
``effective potential'' of the motion of test particles and photons, the
photon escape cones, and the embedding diagrams of t=const sections of
central planes of both the ordinary and optical reference geometry of
these spacetimes. The phenomena are related to the corresponding
phenomena of the Schwarzschild spacetime, and differences caused by the
asymptotic structure of the spacetimes with a nonzero cosmological
constant are discussed. The properties of the embedding diagrams of the
optical geometry are related to the dynamical behavior of test
particles. The limits of the embeddability of the optical geometry are
given and compared with the limits on the outer radius of the interior
solutions of Einstein's equations with a nonzero cosmological constant
for static, spherically symmetric configurations of uniform density. It
is shown that, contrary to the pure Schwarzschild case, these limits do
not fully coincide for repulsive cosmological constants.
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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 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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