Geometric Origin of Gravity: Universal Potential Φ ( R_0 ) = − c^2 and Regular Spacetime

This paper proposes a gravitational framework based on a Geometric Kinematic Model(GKM), aiming to resolve the singularity problem in classical General Relativity. Built upon the fundamental postulate of spatial light-speed helical motion, this model naturally de-rives a primordial gravitational field strength A_0=c^2/R_0, where R_0=GM/c^2 is the characteristic geometric radius. Key Findings: We demonstrate that at the characteristic radius R_0, the gravitational potential satisfies Φ(R_0)=−c^2 . This universal relationship, independent of the source mass, reveals an intrinsic equivalence between gravitational potential energy and rest energy (mc2 ), establishing R_0 as the natural energy zero-point of the gravitational system. Based on this framework, we construct a unified metric that satisfies the weak-field limit and possesses a singularity-free (de Sitter) core at the origin. We prove that this geometric structure can be supported by a self-consistent Nonlinear Electrodynamics (NLE) field source and analytically reconstruct the corresponding Lagrangian. Furthermore, this study offers a thermodynamically self-consistent perspective on the black hole information paradox via an “energy-geometry” conversion mechanism at the R_0 surface. The model maintains mathematical consistency across scales from microscopic particles to macroscopic black holes and yields experimental predictions distinct from standard General Relativity (such as modified black hole ringdown frequencies), providing candidates for verification in future gravitational wave experiments.