On the Mathematical Elimination of Black Hole Singularities

Black hole singularities predicted by the Penrose-Hawking theorems are physically implausible: classical gravitational theories with a constant G inevitably lead to spacetime breakdown and fail to explain microscopic uncertainty. This work proposes a modified framework where the gravitational constant G is treated as a function of interaction separation R and cosmic radius L. We retain the higher-order Maclaurin expansion terms of G discarded in Newtonian gravitation. Results show higher-order terms are negligible at macroscopic scales (consistent with existing observations), while at microscopic scales they induce alternating attractive-repulsive forces that eliminate singularities by preventing zero object separation. Variations of G with cosmic radius L also support a cyclic galactic evolution scenario. This mathematical approach preserves the existing physical framework and provides a consistent singularity resolution.