Influence of Hairy Parameters on Particle Motion and Fundamental Frequencies around Hayward Regular Black Holes

We investigate the particle motion around a hairy Hayward regular black hole, focusing on how the parameters of the model influence the particle motion. The black hole is characterized by five parameters: its mass M, parameter α describing the charge of the black hole, a coupling constant β, parameter η, and a parameter γ describing the hair of the black hole. We examine the instability of circular orbits using the effective potential approach. In this work, we have obtained analytical expressions for the energy and angular momentum of test particles in terms of the parameters characterizing the black hole. We have also examined the innermost stable circular orbits and the effective forces influencing particle trajectories. Furthermore, the study includes an analysis of epicyclic oscillations near the equatorial plane, leading to closed-form expressions for the radial, vertical, and orbital frequencies. The periastron precession frequency has also been investigated in detail. A comparison with the standard Hayward regular black hole has been carried out, highlighting the differences introduced by the additional parameters. Our results indicate that these parameters play a crucial role in shaping the motion of particles, uncovering new and interesting dynamical features.