Nonlinear Geometric Regularization and Entropic Structures in Black Hole Dynamics

This paper presents a novel system for black hole thermodynamics, extending traditional entropy dynamics through irregularity-adaptive metrics. The developed framework incorporates fractal corrections, regularization of divergent components, and quantum effects within dynamically evolving black hole geometries. Key results include: (1) stability of entropy under extreme and exotic conditions, (2) successful handling of pathological singularities and non-smooth boundaries, and (3) robust predictions for entropy behavior in multi-horizon and non-Kerr black holes. These findings establish a comprehensive, universal approach to black hole thermodynamics, surpassing classical limitations and enabling deeper insights into quantum gravitational phenomena.