Entropy-Geometric Branch Weighting and Black Holes: Regime Analysis, Evaporation Structure, and Foundations for the Curved-Space Programme

Papers 1 and 2 of this series developed the Everettian Branch Measure (EBM) plus C=1 framework, establishing an entropy-weighted branch measure, a corresponding effective free-energy formalism, and a covariant curved-space extension with cosmological applications. The present paper examines the implications of this framework for black holes. The central control parameter is the dimensionless entropy ratio Ξ = |ΔS|/k_B, which governs the validity of the perturbative branch-weight construction. Using the Bekenstein–Hawking entropy as an order-of-magnitude proxy pending a first-principles curved-space calculation, we estimate Ξ_BH ∼ S_BH/k_B = 4πGM²/(ħc). This estimate indicates that Ξ_BH ≫ 1 for all astrophysical black holes, placing them far outside the perturbative regime in which the branch-weight formula was derived. We further identify a critical mass scale M* at which Ξ_BH ∼ 1, and show that it lies in the quantum-gravity domain near the Planck scale. The principal result is therefore not a quantitative prediction, but an identification of the regime structure of the theory and of the conditions under which black-hole applications require a non-perturbative treatment. This paper establishes the scope of the black-hole programme within the EBM+C=1 framework and delineates the research steps required for future quantitative analysis based on Schwarzschild and Kerr solutions of the L-θ field equations. Paper 3 of 3 in the EBM+C=1 series.