A Structural Model of the Page Curve from Competing Internal Dynamics

Description This work presents a general and theory‑independent structural model of the Page curve for black‑hole evaporation. The framework is based on two universal tendencies of internal black‑hole dynamics: a spreading component that enhances quantum repulsion, delocalization, and entanglement generation, and a contracting component that enhances gravitational localization, compression, and reduction of entropy capacity. The competition between these components determines the effective evaporation temperature, the entropy capacity of the remnant core, and the entanglement generation rate throughout the evaporation process. The model naturally regularizes the divergence of the standard Hawking temperature, leading to a finite‑size remnant core and producing the characteristic rise, peak, and decay of the Page curve. General conditions for the Page time and the onset of purification are derived from the finiteness of the core entropy capacity and the suppression of late‑stage entanglement generation. Because the framework relies only on generic structural tendencies rather than a specific microscopic theory, it provides a universal and model‑independent approach to the black‑hole information problem.