THE ABÏON METRIC SECOND-ORDER PERTURBATION THEORY

We compute the second-order gravitational perturbation h⁽²⁾₀z for the ABÏON geometry — a weak-field solution to the Einstein equations driven by organized momentum flux (T⁰ⁱ). The calculation decomposes the second-order source tensor into gravitoelectric–gravitoelectric (EE), gravitoelectric–gravitomagnetic (EM), and gravitomagnetic–gravitomagnetic (MM) contributions, following the post-Newtonian formalism of Blanchet & Damour (1989) and Poisson & Will (2014). For the ABÏON 500m reference design (M = 1.61 × 10⁸ kg, J = 3.50 × 10¹³ kg·m²/s, v = 4,243 m/s), the second-order correction yields h⁽²⁾/h⁽¹⁾ ≈ 10⁻¹⁰, determined by the post-Newtonian parameter (v/c)² and independent of the Cooper-pair coherence amplification factor A_Cooper. Three key results emerge: (1) all non-linear corrections are positive — frame-dragging is monotonically increasing with spin, consistent with the exact Kerr solution where the expansion coefficient is +3/2 at second order; (2) the linearized prediction constitutes a rigorous lower bound on the true warp velocity; (3) the breakdown point of perturbation theory is explicit — the binding constraint is the metric–metric self-interaction condition at A_eff ≈ 4.3 × 10²⁵, well above the Tajmar regime (A = 10¹⁸). The linearized analysis presented in the companion paper is therefore not an approximation but the exact answer for the experimentally accessible regime, accurate to 1 part in 10¹⁰. Reproducible Python code is provided as supplementary material. Keywords: second-order perturbation theory, post-Newtonian expansion, gravitomagnetic correction, frame-dragging, non-linear general relativity, Kerr metric comparison, ABÏON metric, momentum-sourced spacetime, warp velocity, linearized gravity validity