Orbital stability and epicyclic motion around a non-commutative black hole

In this study, we probe the motion of test particles in the case of a spherically symmetric non-commutative black hole solution and show how the model parameters affect the motion of particles. By using effective potential methods, we analyzed the stability (stable, unstable) of equatorial circular orbits around the BH solution under discussion. In addition, we derived the exact mathematical equations for the energy and angular momentum of the test particles as a function of the BH parameters. We also study the effective force acting on particles and the innermost stable circular orbits (ISCOs), depending on the model parameters. Epicyclic oscillations are investigated for particles near the equatorial plane and exact relations of radial, vertical, and orbital frequency parameters have also been obtained. We also investigate the periastron precession frequency and the particle collision near the black hole event horizon. Our study explains that the black hole model parameter (Formula presented) significantly influences the results.