SFGE–D-UQAL: A Visco–Elastic, Saturated, and Geometry–Driven Theory of Gravitation

Title: SFGE–D-UQAL: A Visco–Elastic, Saturated, and Geometry–Driven Theory of Gravitation Description: This research presents the SFGE–D-UQAL framework, a comprehensive mechanical-geometric alternative to the Dark Matter hypothesis. While General Relativity and Newtonian mechanics face challenges at galactic scales, this theory proposes that spacetime behaves as a visco-elastic continuum with a finite stress response. Key Components covered in this manuscript: The Universal Mechanical Constant (\Omega_m \approx 1.42 \times 10^{-2}): A fundamental parameter governing the coupling between baryonic mass and spacetime stress. Regulated Shape-Factor (SFGE): A new geometric tool that accounts for the eccentricity and distribution of mass, explaining why spiral and irregular galaxies exhibit different gravitational signatures. Visco-Elastic Displacement (L): Redefining the gravitational interaction as a physical displacement in the spacetime fabric, incorporating memory effects and cosmic damping. Saturation Principle: Utilizing a \tanh-based potential to prevent mathematical singularities in Black Hole cores, aligning gravity with quantum mechanical constraints. Radial Shielding: A mechanism ensuring the theory’s full consistency with Solar System observations and General Relativity at small scales. What this paper solves: Galactic Rotation Curves: Naturally reproduces flat velocity plateaus without the need for undetected particles. Singularity Problem: Provides a "saturated" limit to gravitational strength. The Scale Problem: Bridges the gap between local Newtonian physics and large-scale galactic dynamics through a unified set of Ten Laws of SFGE–D-UQAL. This manuscript is designed for physicists and researchers seeking a falsifiable, mathematically rigorous model that treats gravity as a dynamic, mechanical response of the manifold.