Constraining parameters of Einstein-Power-Maxwell black hole from M87* and Sgr A* data and frequencies analysis with particle dynamics

In this work, we investigate the dynamics of test particles moving in the vicinity of an Einstein–Power–Maxwell black hole characterized by a static, spherically symmetric spacetime. Our analysis focuses on how the motion of these particles is affected by the black hole (BH) parameters. Since such a BH is completely specified by three physical quantities—the electric charge q, the mass M, and a parameter β characterizing the nonlinear electromagnetic sector—we analyze the instability of circular orbits by employing an appropriate effective potential formalism. Specifically, we proceed as follows: (i) we derive analytical expressions for the conserved energy and angular momentum of test particles in terms of the BH parameters; (ii) we examine the properties of the innermost stable circular orbits (ISCOs) and the corresponding effective force acting on the particles; and (iii) we perform a numerical integration of the equations of motion (EOM) to verify the resulting particle trajectories and to explore the possible classes of motion. Furthermore, we study epicyclic oscillations of test particles in the vicinity of the equatorial plane and obtain explicit analytical expressions for the radial, vertical, and orbital frequencies. On this basis, we analyze in detail the periastron precession frequency and its dependence on the BH parameters. Overall, our results indicate that the BH parameters play a crucial role in governing the particle dynamics, leading to distinctive and physically relevant features in their orbital behavior.