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.
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