Time Field Theory XIII: Unified Nature of Second-Order Spacetime Geometry — Intrinsic Connection Between Charge, Gravity, and Gravitational Waves

This work is the thirteenth paper in the Time Field Theory (TFT) series, which systematically establishes a fundamental geometric separation in spacetime structure: first-order spacetime geometry governs mass (the existence intensity of matter), while second-order spacetime geometry governs all fundamental interactions, charge, and gravitational waves. Within the axiomatic framework of TFT, it is rigorously demonstrated that: • Mass originates from the first-order gradient of the time flow rate, representing the accumulated intensity of local spacetime distortion. • Charge corresponds to localized, static second-order topological deformation of spacetime, naturally carrying both polarity (direction) and magnitude (intensity). • Gravitational waves correspond to global, dynamic second-order curvature oscillations of spacetime, propagating as perturbations of the large-scale geometric structure. Charge and gravitational waves are interpreted as observable indicators of structural recasting in the same second-order spacetime potential, manifested at different spatial scales and dynamical regimes. This work unifies electromagnetism and gravity under a single, consistent geometric framework, and proposes several empirically falsifiable theoretical predictions for experimental verification.