The radial acceleration relation (RAR) reveals a remarkably tight correlation betweenthe observed gravitational acceleration in galaxies and that predicted from the baryonicmass distribution. The existence of such a universal relation suggests the presence of acharacteristic acceleration scale governing galactic dynamics.Here we present an Effective Relaxation Model (ERM) in which galactic-scale gravita-tional dynamics are described using an effective relaxation framework characterized by afinite response timescale. The model introduces an effective relaxation timescale of cosmo-logical order, τ ∼ H−1, leading naturally to a characteristic acceleration scale a0 ∼ c/τlinked to the Hubble expansion rate.We show that the resulting quasi-steady effective acceleration law reproduces the ob-served mean RAR, approximately flat galaxy rotation curves, and the baryonic Tully–Fisherrelation without introducing galaxy-dependent dark matter halo profiles or galaxy-specificfitting parameters.The framework is formulated as an effective macroscopic description that remains con-sistent with the weak-field limit of general relativity in high-acceleration environments.While the overall agreement with current observations is encouraging, mild systematicdeviations remain in the deepest low-acceleration regime, suggesting that additional nonlin-ear suppression effects may be required in some low-surface-brightness systems.Overall, the Effective Relaxation Model (ERM) provides a simple, testable, and phe-nomenologically motivated description of low-acceleration galactic dynamics. The presentwork is intended as an effective galactic-scale framework rather than a complete alternativetheory of gravity.
Chang-Sik Kim (Thu,) studied this question.