Global Structure of Saturated Collapse Under Finite Invariant Constraints: Nonlinear Substrate Saturation and Singularity Removal in RST
32. Global Stability of the Saturated Core 32.1 Interior Background Solution Inside the saturation region, the substrate energy density approaches its invariant upper bound: ρ S = ρ max This produces the effective interior metric: ds² = −(1 − H² r²) dt² + dr² / (1 − H² r²) + r² dΩ² with H² = (8πG / 3) ρ max This corresponds to a de Sitter–like core. 32.2 Perturbation Variables Consider perturbations of both the metric and the substrate field: g μν = g μν (0) + h μν S = S 0 + δS The background solution satisfies: β S 0 ³ = σ 32.3 Linearized Coupled System Perturbing the Einstein equations gives: δG μν = 8πG ( δT μν matter + δT μν S ) The substrate perturbation obeys: □ δS + 3β S 0 ² δS = 0 with effective mass: m eff ² = 3β S 0 ² 32.4 Absence of Snyder-Type Instabilities Many regular black hole models exhibit Snyder instabilities due to negative pressure gradients. In RST, the substrate equation of state satisfies: P S = ρ...