Dark Tension Field Framework (DTFF): A Geometric Lens for Dark Sector Dynamics

We introduce the Dark Tension Field Framework (DTFF), a classical general relativity model that investigates geometric contributions to gravitational phenomena typically associated with the dark sector. The framework analyzes curvature-induced geodesic behavior and vacuum energy redistribution near a proposed thin geometric boundary (codimension-one hypersurface) that may arise during gravitational collapse. Such a boundary, constructed using Israel junction conditions and constrained by the Bianchi identities, would serve as a controlled setting for examining effective stress-energy contributions from curvature discontinuities and asymmetric vacuum structure. A companion computational tool demonstrates that, under this framework, supermassive black hole mass alone can predict the characteristic scale of galactic dark halos with empirical accuracy across a diverse galaxy sample. These results highlight a potentially unifying geometric mechanism for halo formation and vacuum-driven expansion, providing a classically grounded, empirically testable perspective on dark sector dynamics that may complement or refine standard cosmological approaches.