Trajectories and high frequencies spectra around charged black holes under anisotropic matter field

In this paper, we investigate the motion of test particles around a charged black hole (BH) immersed in an anisotropic matter field. The underlying spacetime is described by a spherically symmetric line element characterized by the function f (r), where M denotes the mass of the BH, q its electric charge, k the density parameter of the surrounding anisotropic fluid and w the anisotropy index. In addition, this formulation generalizes the Schwarzschild geometry and reduces to it when both q and k vanish. We first analyze the structure of the horizon and the influence of these parameters on the geometry. Then, considering the geodesic motion of particles, we study the effective potential, innermost stable circular orbits (ISCOs), and the corresponding trajectories and effective forces. Furthermore, we tested harmonic oscillations as perturbations of circular motion, derived the oscillation frequencies as measured by both local and distant observers, and examined the periastron precession as a relativistic correction. In addition, the results show the influence of the BH parameters (M, q, k, w) in shaping the particle dynamics, orbital stability, and relativistic frequencies around the BH. In this context, we discuss the physical influence of BH models on our results. At the same time, the numerical results indicate that the oscillations of the accretion-driven shock cone formed around anisotropic charged BHs behave as a natural source of QPOs. The numerically calculated HFQPO frequencies give rise to commensurate ratios of 3: 2 and 2: 1 that are consistent with observations. These numerically obtained ratios and spectral characteristics show good agreement with the observational results reported for BH X-ray binary systems such as XTE J1550-564 and GRO J1655-40. Therefore, these results demonstrate that changes in spacetime parameters in the strong gravitational field contribute to the HFQPO frequencies observed in BH X-ray binary systems.