First-Principle Derivation of the Schwarzschild Radius Based on Time Field Theory (TFT)

This work presents a complete, step-by-step, first-principle derivation of the Schwarzschild radius within the framework of Time Field Theory (TFT). Starting only from the axioms of four-dimensional total speed conservation and spacetime decomposition in flat Euclidean space, we rigorously derive the standard Schwarzschild radius formula r_s = 2GM/c^2 without spacetime curvature, singularities, or auxiliary assumptions. The derivation is mathematically elementary and physically transparent, showing that the Schwarzschild radius corresponds to the critical radial position where the temporal component of the total four-speed vanishes and the spatial component reaches the speed of light c. This paper serves as a fundamental and self-contained result of Time Field Theory.