The flattening of galactic rotation curves remains a central puzzle in modern astrophysics and gravitational theory; existing mainstream explanations largely rely on the dark matter hypothesis and lack support from first principles. Based on a single fundamental axiom and combined with observational facts of galactic dynamics, this paper proposes a dynamic equilibrium mechanism between gravity and the intrinsic expansion effect of space, thereby constructing a galactic dynamical model that does not introduce dark matter. The study demonstrates that gravity can exert a suppressing effect on the intrinsic stretching properties of space, thereby naturally defining the physical concept of the gravitational critical radius: Within the critical radius, gravitational suppression dominates the dynamical behavior; beyond the critical radius, spatial expansion influences the motion of galaxies by altering the radial stretching of space. Gravitational suppression and spatial expansion maintain a dynamic equilibrium, providing a physical mechanism that explains the fundamental cause of the flattening of galactic rotation curves. By establishing a spherically symmetric ideal model, we derive the equilibrium equation for the gravitational critical radius, the critical velocity equation, and the theoretical core coupling relation of the system, thereby naturally reproducing the Tally–Fisher empirical law.Using the Milky Way as a calibration sample, the value of the space-gravity coupling constant was determined to be K ≈ 1.21×10⁻¹⁰ m s⁻² (range: 1.07×10⁻¹⁰–1.36×10⁻¹⁰ m s⁻²). The dimensions of this parameter are consistent with those of acceleration, and its value is close to the characteristic acceleration of Modified Newtonian Dynamics (MOND).Strictly adhering to the principle of parameter-free fitting, we selected a sample of six high-purity, non-interacting standard disk galaxies from the 175 spiral galaxies in the SPARC database for theoretical validation. By comparing the theoretical rotational velocities with the observed values, the results showed that the relative deviations in the sample ranged from 0.67% to 20.75%, thereby verifying the physical consistency and observational compatibility of this model. This theory features a complete logical framework, a clear physical picture, and a concise mathematical structure. Derived from fundamental mechanics and spatial evolution mechanisms, it avoids the artificial assumption of dark matter. It provides a novel, fundamental explanatory framework for the long-standing issues surrounding galactic rotation curves and offers a new theoretical reference for future research in galactic dynamics and the expansion of gravitational theory.This version (v2) updates the full text to English, corrects minor typos, and improves clarity of the discussion section. The original Chinese version (v1) is preserved in the version history.Keywords: galactic rotation curves; intrinsic expansion of space; gravitational critical radius; space-gravity coupling constant; gravitational suppression; Tally–Fisher relation; dark matter-free models; MOND theory
Yao Shen (Wed,) studied this question.