Topological Knot Model for Black Holes: Quantization of Mass and Topological Charge Dynamics

In this paper, a novel model for black holes based on topological knot theory is presented, in which black holes are defined as knots in the fabric of space with a layered structure and different topological phases. Using the structure-charge equivalence principle and Bogomolny's theorem, it is shown that topological charge is an integer and discrete quantity that directly quantizes the mass of the black hole. Solving the hydrostatic equilibrium equation predicts a radial density distribution of the form ρ(r) ∝ r⁻², which is consistent with gravitational lensing data. In this model, black hole instability is defined as a dynamic process in which mass accumulation at the center reduces the topological charge, and when it reaches zero, rupture occurs. Hawking radiation is also interpreted as a reverse process aimed at increasing the central topological charge. Furthermore, the Big Bang is defined as a catastrophic rupture of the entire spatial fabric, in which the total topological charge reaches zero and enormous energy is released; the cosmic microwave background radiation and the expansion of the universe are explained as the remnant and consequence of this rupture, respectively. The model is validated against observational data from 50 supermassive black holes and Planck cosmological parameters, showing excellent agreement (error less than 0.2%). Statistical comparison with standard Schwarzschild and NFW models confirms the superiority of the topological knot model with χ² = 8.2 and ΔlnZ = +2.3, indicating strong evidence in favor of the topological structure of the spatial fabric. This model, without requiring a singularity, provides a unified description of black holes, instability, Hawking radiation, and the Big Bang, and offers testable predictions for high-energy cosmic events and the black hole evaporation process.