QPO tests and charged particles around regular Ayón-Beato-Garcia black holes

In this work, we use an Ayón-Beato-Garca (ABG) black hole solution (BH) obtained in GR coupled to nonlinear electrodynamics (NED), which is regular with the electric charge that could be a candidate astrophysical black hole. First, we derive an expression for the scalar electric field potential. Then, we investigate the circular motion of electrically charged particles using the Hamilton–Jacobi formalism, including the effective potential for circular motion, energy, and angular momentum for circular orbits, as well as the innermost circular orbits (ISCOs). Using equations of non-geodesic motion, we derive equations for radial and angular oscillations and apply them to quasi-periodic oscillations (QPOs) around the ABG BHs. We provide Monte-Carlo-Markov-Chain (MCMC) analyses using QPO data observed around three stellar-mass candidates in the microquasars XTE J1550-564, GRO J1655- 40, and GRS 1915+105, and also the data around an intermediate-mass black hole in the ultraluminous galaxy M82 X-1 and supermassive black hole SgrA* in the Milky Way galaxy. The obtained results demonstrate how the ABG black hole solution can describe astrophysical black holes and enhance the theoretical understanding of QPOs near the black hole, providing insights into the underlying physical mechanisms that govern the motion of charged particles.