An Evoltropic Evolution-Field Framework for Galactic Dynamics and Finite-Curvature Strong Gravity

Abstract

This work develops an Evoltropic Evolution-Field framework in which physical time is interpreted operationally as the measurable rate of physical becoming. A dimensionless scalar Evolution field E(x) is introduced, with a physical lower bound Emin > 0. The paper focuses on two gravitational regimes: galactic dynamics and strong-field curvature. At galactic scales, an effective Evolution deformation is constructed from the baryonic gravitational field. For a finite baryonic mass distribution, the accumulated deformation approaches a finite quantity L∞. A phenomenological Evoltropic acceleration, gE(R) = AE ln(1 + L∞/R), then produces an approximately constant outer circular-velocity contribution, V 2 E,∞ = AEL∞. At strong fields, E is treated as an independent covariant scalar field rather than being identified with a metric lapse. A minimal covariant scalar-field action is introduced, together with its stress-energy tensor and field equation. The regularity analysis shows that a finite central energy density gives m(r) ∝ r 3 and a metric expansion f(r) = 1 − αr2 + O(r 4 ), for which the Kretschmann scalar approaches the finite value K(0) = 24α 2 . This distinction is essential: a nonzero Evolution rate alone does not mathematically prove finite curvature; finite curvature follows from a regular solution of the coupled gravitational and Evolution equations. The Milky Way numerical calculation and the global strong-field boundary-value problem are therefore identified as decisive tests. No claim is made that a complete observationally validated alternative to General Relativity has already been established.