Rethinking Gravity Without Dark Matter: An Effective Area Interpretation of the Inverse-Square Law

This paper is motivated by the long-standing problem of explaining the dynamics of galaxies and galaxy clusters without invoking dark matter. In the standard framework, discrepancies between observed motions and predictions from Newtonian gravity are attributed to additional unseen mass components. While this approach has been widely successful, it also raises the question of whether alternative explanations may exist based on geometry rather than new matter. In this work, we revisit the inverse-square law of gravity from a geometric perspective. Instead of focusing on the source term, we emphasize the role of the effective propagation area over which gravitational influence is distributed. We show that the inverse-square law can be understood as a special case of spherical propagation, where the effective area grows as 4πr24 r²4πr2. By shifting attention to the denominator, we introduce a generalized formulation in which deviations from inverse-square behavior may arise from geometry-dependent spreading. This provides a minimal conceptual framework in which galaxy-scale gravitational phenomena can be explored without introducing additional mass components, and serves as a foundation for more general propagation geometries developed in related work.