Dark tension field framework: Halo dynamics from collapse interfaces in general relativity

We model dark halos as a conserved, nonparticulate, anisotropic stress-energy within classical general relativity. A collapse-born codimension-one interface is treated using Israel junction conditions and standard quasi-local balance laws. Interface data set one-sided boundary values for a static, spherically symmetric exterior, which we evolve using the anisotropic Tolman–Oppenheimer–Volkoff equations. Because pressures gravitate, a weak-field active density (rest-energy density plus pressure terms) sources both rotation curves and lensing; anisotropy permits — but does not require — gravitational slip between the Newtonian-gauge potentials. The exterior is nonvacuum and locally conserved, so Birkhoff’s theorem does not apply. No new particles or modifications to Einstein gravity are introduced. We provide energy-condition checks, thin-shell stability bounds and an admissible closure class for the exterior anisotropy. In a spherical, quasi-static, weak-field regime the framework yields cored inner profiles and a sublinear scaling between supermassive black hole mass and halo size. We introduce a single-calibration, blind estimator that maps supermassive black hole mass to halo size; once a Milky Way–M31 reference pair fixes its constants, all evaluations are out of sample with no per-object tuning. All exterior statements are internal to general relativity and independent of any interior scenario, such as a regular bounce confined to an inner layer.