The Topological Fuzzball Bounce Model: A Unitary Solution to the Black Hole Information Paradox

This paper proposes the Topological Fuzzball Bounce Model, a theoretical framework that resolves the black hole information paradox in a strictly unitary manner. By replacing the classical event horizon with a topological phase transition surface governed by Loop Quantum Gravity spin networks and string theory D One D Five P microstates, we eliminate both classical singularities and information loss. Utilizing effective polymerization and area gap constraints from Loop Quantum Cosmology, we demonstrate that collapsing matter reaches a fundamental Planckian critical density, triggering a quantum bounce via tunneling that transitions the core into a stable white hole state. The long standing issue of runaway remnant energy storage is analytically solved via the holographic Island Formula, where the interior geometry forms an extended non local entanglement island. Finally, microscopic scrambling bounded by the Hayden Preskill limit ensures that information is non thermally released through ultra high frequency gravitational wave spectra, perfectly reproducing the Page curve and upholding quantum mechanical purity. Furthermore, to test the physical consistency of the model, we analyze a thought experiment involving a diary containing information falling into the black hole. The diary crosses the topological horizon smoothly without encountering singularities or firewalls. Its information is then microscopically scrambled within the internal entanglement island and finally released non-thermally through ultra-high-frequency gravitational wave spectra during the white hole phase transition, perfectly upholding global unitary evolution.