Charge-Induced Pole Cancellation and Horizon Transitions in Scale-Dependent Gravitational Collapse

Abstract

We construct a charged Oppenheimer-Snyder-like collapse model in scale-dependent gravity by matching a spatially flat FLRW interior to a charged scale-dependent exterior across a timelike thin shell. The electric charge is confined to the stellar surface, preserving interior homogeneity and isotropy. The exterior geometry is supported by a phenomenological Bianchi-consistent effective source, while the shell dynamics follow from the Israel-Maxwell junction conditions. A barotropic surface equation of state closes the shell system, with a charged-dust shell as the minimal realization. For a negative scale-dependent parameter, $\tilde{\omega}<0$, the exterior contains a finite-radius boundary $x_s$ defined by $D(x_s)=0$. Charge separates the solutions into three regimes. For $0\le q^2<x_s$, the lapse develops a negative pole at a curvature singularity, the physical exterior contains one outer horizon, and a representative monotonic collapse crosses this horizon before reaching $x_s$; no future-directed locally outgoing radial null branch emerges from the singular boundary. At $q^2=x_s$, simultaneous zeros of the numerator and denominator cancel the curvature pole, although the prescribed running coupling remains singular. For $q^2>x_s$, the curvature singularity persists with a positive pole and locally outgoing radial null branches exist. Depending on the physical extremality condition $x_e>x_s$, the exterior may contain two simple horizons, one degenerate horizon, or no horizon. These results show that charge qualitatively changes the singular and horizon structure of scale-dependent collapse and provide model-level evidence for horizon shielding in the negative-pole regime.