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

TL;DR

The paper investigates how stable photon spheres and extremality affect orbital precession near black holes to test the Weak Gravity Conjecture (WGC) in strong-field regimes. Employing a frame-by-frame static mass-evolution approach in static, spherically symmetric spacetimes, it derives geodesic dynamics and periapsis shifts via effective potentials and frequency ratios, with careful treatment of extremal limits. Across models including ModMax, Born-Infeld massive gravity, and ModMax-dRGT-like massive gravity in flat and AdS spacetimes, the authors show that extremality preserves key black hole structures (horizon, unstable photon sphere, vanishing Hawking temperature) and that the periapsis shift remains a meaningful qualitative probe for the WGC. The introduction of a stable external photon sphere (Aschenbach-like effect) yields rich orbital dynamics, including prograde/retrograde transitions and triply-regime behavior near extremality, strengthening the case that periapsis-shift phenomenology can serve as a qualitative observational indicator for WGC viability in strong gravity.

Abstract

While the effects of solar mass change can be neglected in studies of solar periapsis shifts-given the relevant timescales and magnitude of change-the influence of a black hole's dynamic and chaotic mass variation on the Periapsis Shift of test particles in its surrounding spacetime demands a detailed and meticulous investigation. Recognizing that black hole mass variation is inherently a continuous and dynamic process, but the extended timescales required for such variations allow us, to employ a static, frame-by-frame approach. We're assuming constant mass within individual frames, while permitting inter-frame mass evolution to prob the effects of mass loss on orbital dynamics. Using this method, we investigate whether the Periapsis Shift in the extremal limit can serve as evidence for the Weak Gravity Conjecture (WGC), addressing the conjecture's role in preserving black hole integrity during evaporation. Subsequently, we analyze the Periapsis Shift under Aschenbach-like conditions, where a stable photon sphere generates non-monotonic orbital velocity profiles, to assess its dynamical impact on relativistic precession. Finally, we synthesize the combined effects of extremality and the presence of stable photon sphere, revealing profound modifications to the Periapsis Shift profile, including prograde-to-retrograde transitions and radial dependencies. Our results demonstrate that the Periapsis Shift--not merely its magnitude but its qualitative orbital behavior--allows a meaningful experimental probe for the WGC in strong-field regimes.

Figures (19)

• Figure 1: The anomalous precession of Mercury’s perihelion(Figure taken from 1) .
• Figure 2: Metric function: with $M = 1, \gamma = 2,$ for different q's
• Figure 3: Metric function VS temperature at the extreme limit
• Figure 4: (4a): The unstable photon spheres(U-PS) with respect to $M = 1, \gamma = 2,q = 2.718281$ , (4b): the topological potential H(r) for ModMax Black Hole
• Figure 5: (5a): $\beta$ diagram (5b): MSCO localization and space classification with respect to $M = 1, \gamma = 2,q = 0.8$ for ModMax Black Hole