THE ABÏON METRIC STABILITY ANALYSIS

We perform a comprehensive stability analysis of the ABÏON metric — a stationary, axially symmetric solution to the linearized Einstein field equations sourced by organized momentum flux (T⁰ⁱ) rather than energy density (T⁰⁰). The analysis evaluates seven independent stability criteria: ergoregion formation, Lichnerowicz mode stability, Chandrasekhar–Friedman–Schutz (CFS) instability, superradiant amplification, gravitational-wave emission timescale, Friedman's canonical energy theorem, and the Rayleigh criterion for differential rotation. For the reference ABÏON 500m design (M = 1.61 × 10⁸ kg, J = 3.50 × 10¹³ kg·m²/s, ω = 30 rad/s), all seven criteria yield unconditional stability in every experimentally accessible regime (A_Cooper ≤ 10¹⁸, Q ≤ 10¹¹), with safety margins ranging from 10⁸ to 10²⁶. The most powerful result is Friedman's theorem: because the ABÏON spacetime is stationary, asymptotically flat, and contains no ergoregion — with |h₀z| ≤ 1.9 × 10⁻⁸ even at maximum Tajmar amplification, eight orders of magnitude below the ergoregion threshold — the canonical energy of any linear perturbation is positive definite, and mode stability follows as a proven theorem of general relativity. All instability thresholds cluster at A×Q ≈ 10²⁵⁻²⁶, coinciding with the breakdown of the linearized approximation itself (A×Q ≈ 4.3 × 10²⁵ from the metric–metric self-interaction condition). Within the domain of validity of linearized GR, the ABÏON solution is unconditionally stable. Reproducible Python code is provided as supplementary material. Keywords: frame-dragging, gravitomagnetism, linearized general relativity, metric stability, ergoregion, CFS instability, Friedman theorem, canonical energy, Lense-Thirring effect, ABÏON metric, momentum-sourced spacetime, warp metric