Motion of test particles in a regular black hole space–time

We consider the motion of test particles in the regular black hole space-time given by Ayón-Beato and García [Phys. Rev. Lett. 80, 5056 (1998)]. The complete set of orbits for neutral and weakly charged test particles is discussed, including for neutral particles the extreme and over-extreme metric. We also derive the analytical solutions for the equation of motion of neutral test particles in a parametric form and consider a post-Schwarzschild expansion of the periastron shift to second order in the charge.