Time Field Theory: Velocity-Gravity Coupling and the Logical Inconsistency of General Relativity

Based on the core axiom of total spacetime speed conservation c² = vₜ² + vₛ² in Time Field Theory (TFT), this paper presents rigorous mathematical derivations to establish the intrinsic coupling mechanism between spatial velocity and gravitational effects. TFT defines gravity as the spatial gradient of the local time flow rate rather than spacetime curvature. By analyzing General Relativity (GR) using its own logical framework, we demonstrate a fundamental structural inconsistency: although GR theoretically recognizes kinetic energy as part of the gravitational source, its mathematical formalism and practical applications artificially separate the influence of test particle velocity on the gravitational field. TFT naturally unifies velocity and gravity through the intensity factor 1/γ², yielding a self-consistent description valid in both low-speed and ultra-relativistic regimes. This framework resolves the inconsistency of GR and provides a physically intuitive, mathematically concise foundation for gravitational theory.