Time like geodesics for five-dimensional Schwarzschild and Reissner–Nordström anti-de Sitter black holes

Abstract

Abstract The time like structure of the five-dimensional Schwarzschild and Reissner–Nordström anti-de Sitter black holes is studied in detail. Different kinds of motion are allowed and studied by using an adequate effective potential. Then, by solving the corresponding equations of motion, several trajectories and orbits are described in terms of Weierstraß elliptic functions and elementary functions for neutral particles.