Periodic Orbits of Test Particles in Spherically Symmetric Spacetimes

Abstract

In this dissertation, weiinvestigate the periodic orbitsiof the massive particlesiaround three distinct spacetimes: Schwarzschild black hole, Fisher/Janis-Newman-Winicour (F/JNW) spacetime, and Modified Gravity (MOG) black hole. We derive the geodesic equations using both Hamiltonian and Lagrangian methods. We analyze the effective potential which is an importantifactor in studying the trajectories of orbits. Then, we thoroughly analyze the innermost stable and innermost bound circular orbits. We have establish the periodic orbits using the framework outlined by Levin and Perez-Giz [1]. It demonstrates that by numerically solving q for the periodic orbits, we identify that each orbit corresponds to a unique energy value. In comparison to periodic orbits aroundithe Schwarzschild blackihole, it is observed that lower energies are generally required forithe same orbitsiin F/JNW spacetime and the MOG black hole. This work contributes to a deeper understanding of orbital dynamics in these spacetimes and offers insights into theibehavior of massive particles in various gravitationalifields. IX