The Influence of Stable Photon Sphere Advent on Orbital Precession in moving towards the Extremality

Abstract

In this work, we investigate the behaviour of the periapsis shift in static charged black-hole spacetimes, focusing on the interplay between extremality and the Aschenbach-like effect. We first examine the evolution of orbital dynamics as the extremal limit is approached in representative charged black-hole models. We then extend the analysis to black-hole geometries that admit a stable photon sphere outside the event horizon, where the Aschenbach-like effect has previously been identified. Our results show that the periapsis shift remains a well-defined dynamical quantity in the extremal regime and continuously reflects changes in the underlying spacetime geometry. For black-hole solutions possessing an external stable photon sphere, the associated minimum of the effective potential produces characteristic modifications in both the angular-velocity profile and the periapsis shift. When extremality and the Aschenbach-like effect coexist, the orbital dynamics undergo a qualitative transition, giving rise to a three-region structure consisting of an inner prograde region, an intermediate retrograde region, and an outer prograde region. Within the black-hole models investigated in this work, such behaviour is absent from the other configurations considered. These results demonstrate that the periapsis shift provides a sensitive dynamical probe of strong-field black-hole spacetimes, encoding both geometric and orbital information beyond that obtained from photon-sphere analyses alone. Our findings highlight the rich orbital structure that can emerge from the combined presence of extremality and an external stable photon sphere and provide a useful framework for future studies of orbital dynamics in modified theories of gravity.