Properties of the Reissner-Nordstr\"om Spacetimes with a Nonzero Cosmological Constant

Properties of the Reissner-Nordstr\"om black-hole and naked-singularity spacetimes with a nonzero cosmological constant are represented by their geodetical structure and embedding diagrams of the central planes of both the ordinary geometry and associated optical reference geometry. Motion of test particles and photons is described in terms of an appropriate `effective potential.' Circular geodesics are discussed and photon escape cones are determined. In all asymptotically anti-dS black-hole spacetimes and some asymptotically dS black-hole spacetimes a region containing stable circular geodesics exists, which allows accretion processes in the disk regime. The inner region is limited from below by particles with zero angular momentum that are located in stable equilibrium positions. The inertial and gravitational forces related to the optical reference geometry are introduced and specified for the circular motion. It is shown how the properties of the centrifugal force are closely related to the properties of the optical reference geometry embedding diagrams.