Topological Conservation in Kerr Black Hole Evaporation and the Kerr–Planck Core: A Unified Framework for Quantum-Gravitational Remnants and Cosmogenesis

This paper presents a unified theoretical framework for the terminal state of Kerr black hole evaporation, grounded in topological conservation principles. We demonstrate that classical complete evaporation to asymptotically flat spacetime is incompatible with the preservation of key topological invariants of the rotating Kerr geometry, including the U(1) spin-bundle structure, nontrivial first Chern class, and angular-momentum fibration. Extending semiclassical arguments into the Planck regime, we propose that evaporation ends in a stable quantum-gravitational remnant: the Kerr–Planck core. This core preserves irreducible angular momentum J_core ≈ ℏ, saturates spacetime curvature at the Planck scale (K ∼ 1/ℓ_Pl⁴), and retains the topological information of the progenitor black hole. The framework is compatible with the Generalized Uncertainty Principle (GUP), Asymptotically Safe Gravity, and loop-quantum-gravity bounce scenarios. We derive the core’s characteristic temperature T_core ≈ 7.5 × 10^{29} K, which aligns naturally with Grand Unification (GUT) scales. A Chern–Simons contribution arising from the core’s topological structure stabilizes the Euclidean instanton action at B ≈ 137, reproducing the inverse fine-structure constant α_QED^{-1} ≈ 137.036 to within 0.006% without fine-tuning. This remnant provides the physical foundation for the rotating Kerr–Planck core cosmology developed in the preceding series [1–4], linking black-hole evaporation, quantum-gravitational decoherence, and cyclic cosmogenesis. The model predicts testable signatures including CMB low-ℓ anomalies (ℓ = 3–8), non-local large-scale structure correlations at ∼1.8–2.1 Gpc, tensor-to-scalar ratio r ≈ 0.004, and residual frame-dragging effects, observable with upcoming surveys (Euclid, DESI, CMB-S4).