Evolution Current Gravity

We propose a theoretical framework in which gravitation is represented fundamentally by an Evolution current propagating through an invariant, stationary nodal lattice rather than by a literal inward motion of space. The framework is motivated by the Painlevé–Gullstrand (PG) representation of the Schwarzschild solution, but assigns a different physical interpretation to its shift field. The underlying lattice coordinates remain stationary, while an inward Evolution-current field uE(r) is associated with the mass-energy distribution. In the exterior vacuum region, the proposed current magnitude reduces to the PG/Schwarzschild relation u2E = 2GM/r, so that the Schwarzschild exterior is recovered exactly as an effective metric description. For an extended spherical source, however, the relevant source is the enclosed mass m(r), not the total mass M. For a regular central density, m(r) ∼ r3, implying uE(r) ∼ r and g(r) ∼ r near the center; consequently both the net gravitational accelerationand the Evolution current vanish at the exact center rather than diverging. We introduce a normalized Evolution-rate field E(r) and a logarithmic potential possessing a strictly positive minimum Emin > 0. This supplies a phenomenological saturation mechanism intended to prevent the Evolution rate from reaching zero and to permit finite central density and curvature. We derive the weak-field, exterior, and regular-center limits, formulate a coupled mass–Evolution-field system, and identify the conditions required for a numerical boundary-value solution. The paper does not claim that the proposed interior solution has yet been established: the nonlinear matching problem remains a quantitative test of the framework.The principal result is therefore a falsifiable mathematical construction that reproduces the known Schwarzschild exterior while providing a distinct underlying interpretation and a possible route to nonsingular compact objects.