GERT and Black Holes: Macroscopic Phase Transition in the Hyperdilute Universe

Background: The late-time fate of black holes and the operational limits of General Relativity (GR) in the far future remain open problems in thermodynamic cosmology, and are central to the causal gap discussed in Penrose’s conformal framework. Objective: We determine, within Gibbs Energy Redistribution Theory (GERT), the lower density boundary of GR validity and the thermodynamic fate of supermassive black holes in the Hyperdilute Regime. Methods: Using the asymptotic gas-dominated GERT term, we derive the critical crossing λ_CMB(a) = H⁻¹(a), compute a_crit and ρ_GR,min analytically, and evaluate black-hole thermodynamic states (in cluding ∆G and inversion scales) across mass ranges, with no additional premises beyond the base framework. Results: We obtain a_crit = 10^12.88±0.12 and log₁₀(ρ_GR,min) = −65.2 ± 0.4 kg/m³, closing the Layer 3 validity domain from Planck density to a symmetric lower operational threshold (161.9 density decades). At acrit, all black holes with M > M^∗ ≈ 1.7×10⁵ M⊙ are in thermodynamic absorption, with strongly non-spontaneous redistribution (e.g., ∆G ≈ +5800 Mc² for 10⁹ M⊙). Thermal inversion occurs later in the Quasi-Vacuum, where cosmological cooling outpaces Hawking thermal change by ∼10¹⁰⁶; at a_inv(M), supermassive-black-hole Schwarzschild radii exceed the Hubble radius by factors of 4 to 10¹⁰. Conclusions: In this regime, Hawking evaporation is not the operative end-channel for high-mass black holes. GERT instead identifies a Gibbs-driven macroscopic phase transition (∆G < 0 in the Quasi-Vacuum) and establishes a symmetric but dynamically inverted boundary structure for Layer 3: Inward-dominated at emergence (dH/da < 0) and Outward-dominated at dissolution (dH/da > 0). This provides a quantitative thermodynamic completion scenario and a causal contribution to the CCC end-state problem.