Motti Intermediate Physics — HAL: Towards the Dynamical Closure of Gap 1 — Coherential Field Excitation During Binary Black Hole Merger

Gap 1 of the HAL programme requires demonstrating that the Goldstone field theta injects J_theta = (C0^3-1)/C0 * J_GR ~ 3*alpha_em * J_GR during binary black hole merger. During inspiral, theta is excited perturbatively giving J_theta ~ alpha_em^2 * J_GR — insufficient by factor 400. The injection must occur during the non-linear merger. We derive the exact NR consistency condition: mean square amplitude of theta during merger must equal 3*alpha_em*(GM/c^3)^2/(8*pi). A backreaction estimate gives 94.4% of this target, identifying backreaction as the correct physical channel. The exact factor requires numerical relativity.