Gas-Poor Galaxies Show Competitive Linear Gravity Against Dark Matter: A SPARC Survey Analysis

We analyze rotation curves from 175 galaxies in the SPARC database to test linear gravity (𝐹 ∝ 1/𝑟) against standard Newtonian gravity with dark matter (𝐹 ∝ 1/𝑟² + DM). While dark matter provides superior fits for 85% of galaxies, we identify a significant subset (15%, n=25) where linear gravity is competitive. Crucially, we find a statistically significant correlation: galaxies where linear gravity performs competitively have systematically lower gas-to-stellar mass ratios (0.13 ± std) compared to dark matter-dominated galaxies (0.18 ± std), with p = 0.023 (Student’s t-test). No significant correlations were found with total mass, distance, or morphological type. We interpret this pattern within a multi-scale gravity framework where concentrated stellar matter exhibits linear gravity signatures while diffuse gas requires effective dark matter. This suggests a fundamental difference in gravitational behavior based on matter density and distribution, potentially related to dimensional projection effects in higherdimensional theories. Our results validate the dark matter paradigm for most galaxies while identifying a distinct subset warranting further investigation.