Publication date: Aug 1999
Abstract:
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.
Authors:
Stuchlík, Z.; Hledík, S.;