Information Preservation in Schwarzschild Black Holes: A Theoretical and Computational Study

One of the most profound dilemmas in modern theoretical physics is the 'Black Hole Information Paradox,' which emerges at the intersection of Quantum Mechanics and General Relativity. The principle of 'Unitarity,' which forms the foundation of Quantum Mechanics, posits that information can never be destroyed and that the initial quantum state of any system is theoretically reversible. Conversely, within the framework of General Relativity, black holes are defined as absolute traps from which no information that has crossed the event horizon can escape. Although the mechanism of Hawking Radiation demonstrates that black holes lose mass by emitting thermal radiation and ultimately evaporate, the assumption that this radiation does not carry information leads to the conclusion that information is irrevocably lost alongside the black hole.This study investigates this paradox under the title 'Information Conservation in Schwarzschild Black Holes: Theoretical Modeling and Computational Simulation'. Within the scope of this research, the relationship between Bekenstein-Hawking entropy and Von Neumann entanglement entropy for Schwarzschild metrics is analyzed through numerical simulations. In this study, the entropy evolution during the evaporation process of the black hole is modeled by referencing the Page Curve, which represents the scenario where information conservation is maintained. By quantitatively comparing the classical Hawking scenario (information loss) with the Page scenario, which preserves unitarity, the thermodynamic consistency of the information recovery process is discussed.