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

This paper explores how stable photon spheres and extremal black hole conditions influence orbital precession, proposing that periapsis shift behaviors can serve as experimental tests for the Weak Gravity Conjecture in strong gravitational fields.

Contribution

It introduces a novel analysis of periapsis shift modifications due to stable photon spheres and extremality, linking orbital dynamics to fundamental quantum gravity conjectures.

Findings

Stable photon spheres cause non-monotonic orbital velocity profiles.

Extremality and photon spheres lead to prograde-retrograde transition in periapsis shift.

Periapsis shift behavior can serve as an experimental probe for the Weak Gravity Conjecture.

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.