Page Curve from Gravitational Memory Saturation: A Real-Time Mechanism for Black Hole Information Recovery

We propose a non-Markovian dynamical framework for black hole evaporation in which information recovery emerges from temporal correlations encoded in a memory kernel derived from an adiabatic bath coupling. The model provides an effective real-time description of information flow and generates a Page-like entropy evolution without invoking replica wormholes or island prescriptions. Crucially, we show that the Page time arises as a universal consequence of the unitarity normalization condition, without parameter tuning. We go beyond the Markovian approximation by analyzing finite correlation time effects; numerical integration demonstrates that the Page point is robust under non-Markovian corrections, with a shift of approximately $5%$ when the correlation time reaches $1%$ of the evaporation time. Our results suggest that information recovery can be understood as a temporal nonlocal phenomenon with finite memory bounds, offering an alternative perspective on the microscopic origin of unitarity in black hole evaporation. The exponential memory kernel is derived from a microscopic system–environment model using the Feynman–Vernon influence functional, ensuring consistency with open quantum systems and effective field theory expectations.