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

Abstract

Papers 1 and 2 of this series developed the Everettian Branch Measure (EBM) plus C=1 framework. The present paper examines implications for black holes. Using the Bekenstein-Hawking entropy as an order-of-magnitude proxy, we estimate Ξ_BH ~ S_BH/k_B = 4πGM²/(ℏc), finding Ξ_BH ≫ 1 for all astrophysical black holes — far outside the perturbative regime in which the branch-weight formula was derived. We identify a critical mass scale M* at which Ξ_BH~1, showing it lies in the quantum-gravity domain near the Planck scale. The result is an identification of the theory's regime structure, not a quantitative prediction. v2 correction (Aug 2026): this paper's second estimate of M* (~30 mg), derived from Paper 1's soliton benchmark, is corrected: that benchmark has since been shown to correspond to a saddle-point configuration rather than a stable soliton and is now illustrative only. The primary, entropy-based estimate (M*≈0.006 mg, from Ξ_BH=1 directly) does not use the soliton benchmark and is unaffected — it is now this paper's sole well-motivated estimate. The previously-stated "bracketed mass range" (0.006–30 mg) is corrected to reflect that these were never two independently corroborating calculations. The paper's principal conclusion (astrophysical black holes lie far outside the perturbative regime) is completely unaffected.