On the Dynamical Stability of Astrophysical Rings

he purpose of this paper is to consider the ring systems in the context of a modified gravity theory.
In fact, the gravitational stability of a ring system consisted of N particle with the same mass m rotating around a massive object at the center is studied. After finding the equation of motion and considering the dynamics of the system in the equilibrium state, perturbative analysis is used in order to find the linearized version of the equations of motion. Finally using the Fourier analysis, the dispersion relation of the system is derived. At the end, using the observational values of the free parameters of the above mentioned theory and also the dispersion equation the stability criterion of the system for several cases is derived. Finally, the results have been compared with the corresponding results in Newtonian gravity