Information Black Holes and Information Horizons: A Geometric Framework Based on Infinite-Dimensional Information Theory

We develop a geometric theory of information black holes and information horizons based on the infinite-dimensional information manifold of smooth probability densities. Using the Fisher--Rao metric and the information Ricci flow, we define information curvature, information singularities, and information horizons. We derive an information area law, an information surface gravity, and an information analogue of Hawking radiation. Several original equations are introduced, includingthe information horizon equation, the information surface gravity formula, and the information Hawking temperature. This work provides a mathematically rigorous and conceptually unified framework for understanding black hole thermodynamics from the perspective of information geometry.