Some properties of the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes - art. no. 044006

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 c ones, 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 s pacetime, and differences caused by the asymptotic structure of the spaceti mes with a nonzero cosmological constant are discussed. The properties of t he 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 cons tant for static, spherically symmetric configurations of uniform density. I t is shown that, contrary to the pure Schwarzschild case, these limits do n ot fully coincide for repulsive cosmological constants. [S0556-2821(99)0571 4-8].