Probing the regular Ayón–Beato–García spacetime by precessing motion

Abstract In this paper, we investigate the precessing motion around the regular Ayón–Beato–García (ABG) black hole, characterized by an electric charge parameter q . We derive the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in this spacetime, expressing it explicitly in terms of the particle’s orbital energy and angular momentum, as well as the mass and the electric charge. Through detailed analytical calculations, we quantify the charge-dependent modifications to key orbital characteristics, including: (i) the periastron advance, which exhibits a q 2 -correction at 1PN and 2PN orders; (ii) the orbital period, where the charge contribution emerges at a 2PN level. Our results demonstrate that the ABG black hole’s electric charge significantly alters these observables compared to the Schwarzschild case ( q = 0), providing a theoretical framework to test regular black hole models through precision measurements of relativistic orbits. The derived 2PN solution may be applicable to astrophysical systems involving charged compact objects.