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 and utilizing the geometrically

renormalized lattice spacing (a≈0.77lP ), we derive a ”Geometric Evaporation” mode where

the lattice tension drives horizon recession. Correcting for the vacuum stiffness derived in our

renormalization framework, we find the velocity scales as R≈−c4 (a/R), yielding a decay law

of τ ∝M2. We identify the lattice correlation length Lcorr with the hadronic scale (≈1.3

fm), derived from the vacuum’s elastic stiffness. This ”Peierls Locking” ensures that the

rapid geometric channel dominates for PBHs, resolving abundance constraints, while leaving

astrophysical black holes stable.