Kerr–Newman in Boyer–Lindquist coordinates: full certificate on the exterior domain

Kerr–Newman in Boyer–Lindquist coordinates: full certificate on the exterior domain

For M > 0 and all real a, Q. Coordinates (t, r, θ, φ) = (x⁰, x¹, x², x³); Σ = r² + a² cos²θ, Δ = r² − 2Mr + a² + Q². Metric gKN: g_tt = −(Δ − a² sin²θ)/Σ, g_tφ = g_φt = −a(2Mr − Q²) sin²θ/Σ, g_rr = Σ/Δ, g_θθ = Σ, g_φφ = sin²θ((r² + a²)² − a²Δ sin²θ)/Σ; giKN its certified inverse; field faradayKN a Q = dA with A = −(Qr/Σ)(dt − a sin²θ dφ) (faraday_eq_extD). Statement: EinsteinMaxwellCertificate (gKN M a Q) (giKN M a Q) (faradayKN a Q) (domKN M a Q), domKN = {rPlus < r, 0 < θ < π}, rPlus = M + √(M² − a² − Q²) with Real.sqrt (= 0 for a negative argument).

Scope. Every M > 0, every real a, Q (a = 0, Q = 0 allowed). Physical black-hole exterior interpretation adopted in this release: a² + Q² < M² (rPlus = outer horizon radius). At a² + Q² = M², rPlus = M is likewise a (double) root of Δ = (r − M)². For a² + Q² > M² the threshold rPlus = M is not a root of Δ; the certificate then states exactly the printed regular-coordinate domain. No horizon or global theorem.

中文摘要 KN（BL 坐标）对 M>0 与任意实 a、Q，在 domKN = {r₊ < r, 0<θ<π} 上的完整 Einstein–Maxwell 证书。