First derivation of an ECO reflective surface position from a physical scalar field equation in Kerr geometry. The modulus field φ (r, θ) is solved numerically in the full Kerr background for spins a* ∈ 0, 0. 99. The radial kinetic term dominates the angular term by a factor 47–412 near the horizon. The surface φ=φcrit is spherically symmetric to <10^-15 angular variation for all spins. Validates Paper 22 ratio table exactly. No angular broadening of GW echoes. First principles derivation — no free parameters.
Marc López Sánchez (Fri,) studied this question.