Schwarzschild and Kerr Metrics from the Micropolar Cosserat Mechanics of the H4 Crystalline Vacuum

The dynamics of strong-field spacetime and quantum vacuum boundary conditions are derived from the solid-state mechanics of a discrete four-dimensional Cosserat continuum. The vacuum is modeled as the H4 (600-cell) crystalline lattice, in which the extreme 120-vertex coordination enforces Maxwell’s rigidity, blocking affine deformation and forcing structural relaxation strictly through non-affine micropolar microrotations. Kinematic condensation of the Cosserat stiffness tensor yields an effective Poisson ratio of νef f = −1, establishing auxetic spatial curvature as the mechanical origin of the Schwarzschild grr com ponent. Extending to rotational dynamics, we model macroscopic spin as a gravitomagnetic torsional defect current, recovering the exact Lense-Thirring profile Ω = 2GJ/c2r3 from 4D angular momentum flux conservation. In the quantum regime, the lattice grain δ = 1/120 acts as a physical UV cutoff; applying the Euler-Maclaurin formula to the discrete phonon spectrum recovers the exact Casimir force coefficient ℏcπ2/240a4 without renormalization. Finally, Einstein-Rosen bridges are identified as macroscopic dislocation lines whose traversal velocity c · α4 enforces the No-Communication Theorem with a margin of 2.24 × 10^8, providing a mechanics realization of the ER=EPR conjecture. Together these results suggest that spacetime geometry and quantum boundary conditions are emergent properties of a frustrated crystalline vacuum. Email: h4collaboration@protonmail.com