The Torsional Illusion: Resolving the CDM Paradox through Vacuum Topology and Kerr Boundary Dynamics

The Cold Dark Matter (ΛCDM) paradigm relies on the ad hoc insertion of invisible, non-baryonic mass to justify the kinematic anomalies of spiral galaxies, particularly flat rotation curves. However, this phenomenological solution ignores the geometric and topological properties of the 4-dimensional spacetime vacuum. In this work, we resolve the CDM paradox by replacing the dark matter hypothesis with the torsional topology of the vacuum. By moving beyond the torsion-free Levi-Civita metric in favor of a Riemann-Cartan spacetime, we demonstrate that the Kerr horizon of central supermassive black holes imprints a long-range torsional tension (k_T) along the galactic equatorial plane. This non-dissipative "topological current", sustained by the scaling invariance of the 4D continuum, modifies the geodesic balance equation, generating an asymptotic constant velocity v = sqrt(k_T) at large distances. Applying our derivation to the kinematic data of NGC 3198 and Andromeda (M31), we confirm that peripheral rotation curves are a purely geometric consequence of vacuum rigidity. This approach definitively eliminates the cosmological need for dark matter, naturally derives the Baryonic Tully-Fisher Relation (M_bar ∝ k_T^2), and naturally resolves the galactic Cusp-Core problem.