The Influence of Stable Photon Sphere Advent on Orbital Precession in moving towards the Extremality: Periapsis Shift as a Gateway to the Weak Gravity Conjecture

While the effects of solar mass change can be neglected in studies of solar periapsis shifts, the influence of a black hole’s dynamic mass variation on the periapsis shift of test particles demands careful investigation. Using a frame-by-frame adiabatic approximation, we investigate whether the periapsis shift in the extremal limit can serve as a consistency test for the Weak Gravity Conjecture (WGC). We analyze the periapsis shift under Aschenbach-like conditions, where a stable photon sphere generates non-monotonic orbital velocity profiles. Finally, we synthesize the combined effects of extremality and a stable photon sphere, revealing profound modifications including prograde-to-retrograde transitions and triple-regime orbital structures. Our results demonstrate that the periapsis shift-not merely its magnitude but its qualitative orbital behavior-provides a meaningful experimental probe for the WGC in strong-field regimes.