**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.;