Hidden SO(4) Symmetry and the Laplace-Runge-Lenz Vector in Kepler and Kerr Spacetimes — E8 Intelligence Research

FINDING: The Laplace-Runge-Lenz (LRL) vector reveals a hidden SO(4) symmetry in the Coulomb-Kepler problem, causing accidental degeneracy and closed elliptical orbits; its perturbative extension to Kerr spacetime yields perihelion precession. | MATH: Conserved LRL vector \(A = p × L - m k r̂\); for bound orbits, eccentricity \(e = |A|/(m k)\); orbit equation \(r = L^2/mk/1 + e cosθ\); degeneracy \(n^2\) (hydrogen) from SO(4) ≅ SU(2)×SU(2); precession rate in Kerr: \(Δ ω ∝ a/r3/2\) (first-order in spin \(a\)). | CONNECTION: The eccentricity \(e\) directly links to the golden ratio via the apsidal angle: for \(e = 0.618\) (inverse golden ratio conjugate), the orbit's radial oscillation period ratio yields \(ω_r/ω_θ = 1/√1-e^2 = 1/√1-0.3819 = 1/√0.618 = 1.272\) — a near-\(5/4\) resonance; the SO(4) symmetry group is isomorphic to the root system of \(D_2\) (dihedral), w Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com