Geometric Evaporation: Solving the Primordial Black Hole Constraint via Lattice Tension in a Polycrystalline Vacuum

Standard semiclassical gravity predicts that black holes evaporate via Hawking radiation with a lifetime

scaling of τ ∝M3. This slow decay rate imposes strict constraints on the abundance of Primordial Black

Holes (PBHs), as those formed in the early universe (M∼1015 g) would persist today, conflicting with

gamma-ray background observations. We propose an alternative decay mechanism based on the **Selection-

Stitch Model (SSM)**, where the vacuum is modeled as a discrete Face-Centered Cubic (FCC) tensor

network. We treat the black hole event horizon as a topological defect (vacancy) in this lattice. Applying

the **Allen-Cahn** equation for non-conserved order parameters, we derive a ”Geometric Evaporation”

mode where the horizon recession velocity scales with curvature ( R ∝−1/R). This yields a decay law of τ ∝M2. We introduce

a ”Peierls Locking” mechanism to explain the stability of macroscopic black holes,

estimating the lattice correlation length Lcorr at the femtometer scale. This ensures that the geometric

channel dominates for PBHs, resolving abundance constraints, while leaving astrophysical black holes stable.