Simulation of geodesic trajectory of charged BTZ black holes in massive gravity

In order to classify and understand structure of the spacetime, investigation of the geodesic motions of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of geodesic motions in three-dimensional spacetime. We investigate the geodesics near charged BTZ black holes and then generalize our prescriptions to the case of massive gravity. We show that electric charge is a critical parameter for categorizing the geodesic motions of both lightlike and timelike particles. In addition, we classify the type of geodesics based on the particle properties and geometry of spacetime.