Galactic Rotation Curves Explained in the 4DEU Framework by 3D Spatial Curvature from Local Gravitational Blocking of Cosmic Expansion: No Need for Dark Matter

The observed near flatness of galactic rotation curves has long been interpreted as evidence for large amounts of non-baryonic dark matter. Here we show that this phenomenon can be fully explained within the Four-Dimensional Electromagnetic Universe (4DEU) theory. In this framework, gravitation arises from curvature confined to the three-dimensional (3D) spatial hypersurface of a four-dimensional (4D) universe. The so-called “dark halo” does not correspond to any new form of matter but to the intrinsic 3D spatial curvature produced by the gravitational constraint that locally blocks only the 3D component of the 4D cosmic expansion within gravitationally bound systems. Using a Hamiltonian formulation restricted to static spatial slicing (vanishing extrinsic curvature), the effective density sourcing the curvature naturally separates into a baryonic term and an additional geometric contribution associated with the constraint. To test this hypothesis quantitatively, we analyzed the rotation curves from the entire SPARC database, selecting the 129 galaxies that satisfy the statistical and physical quality criteria defined in the method section. The extra-velocity component $v_{\text{extra}}=\sqrt{v_{\text{obs}}^2？v_{\text{bar}}^2}$ was fitted in log-log space with the relation $v_{\text{cve}}\left(r\right)=V_0{\left(r/R_{\text{ref}}\right)}^{\epsilon /2}$ , where $v_{\text{cve}}\left(r\right)$ denotes the extra velocity component predicted by the 4DEU model, corresponding to the extra-baryonic