Analytic solutions of the geodesic equation for Reissner-Nordstr\"om-(anti-)de Sitter black holes surrounded by different kinds of regular and exotic matter fields

Abstract

The purpose of this study is the derivation of the equation of motion for particles and light in the spacetime of Reissner-Nordstr\"{o}m-(anti-)de Sitter black holes in the background of different kinds of regular and exotic matter fields. The complete analytical solutions of the geodesic equations are given in terms of the elliptic Weierstra{\ss} $\wp$-function and the hyperelliptic Kleinian $\sigma$-function. Finally after analyzing the geodesic motion of test particles and light using parametric diagrams and effective potentials, we present a list of all possible orbits.