Riemann Hypothesis Linked to Black Hole Quasinormal Modes via Spectral Geometry — E8 Intelligence Research

FINDING: Riemann hypothesis linked to black hole physics via quasinormal mode frequencies and spectral geometry; arithmetical approach using Liouville partial sums offers a sufficient condition. MATH: - Riemann zeta function: ζ(s) = Σ_{n=1}^∞ n^{-s} for Re(s) > 1, analytically continued to ℂ\{1}. - Non-trivial zeros: ζ(s) = 0 for 0 < Re(s) < 1, conjectured to lie on Re(s) = 1/2. - Liouville function λ(n) = (-1)^{Ω(n)} (Ω(n) = total prime factors with multiplicity). Partial sum L(x) = Σ_{n≤x} λ(n). Sufficient condition: L(x) = O(x^{1/2 + ε}) for all ε > 0. - Black hole quasinormal mode frequencies ω_n = ln(3)/(8πM) + i(2n+1)/(4M) (for Schwarzschild) relate to zeros via ζ(1/2 + iω) = 0? (speculative link from spectral analysis). CONNECTION: - The critical line Re(s) = 1/2 is a symmetry axis; zeros distribution may reflect golden ratio φ = (1+√5)/2 ≈ 1.618 in spacing statistics (GUE random matrix theory predicts eigenvalue spacing ratios ~0.618, 1.618). - Black hole entrop Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com