arXiv2026
A smooth Bianchi I spacetime satisfying the null convergence condition in every null direction is static if it contains a single null geodesic complete to both the past and the future. We prove this result for a general spatial metric, allowing non-diagonal evolution and arbitrary signs of the principal expansion rates. The proof starts from affine Raychaudhuri evolution. On a complete generator of a regular twist-free congruence, nonnegativity of an independent or fixed-ratio sharp-cutoff lower limit forces the full optical tensor to vanish. Dilated square weights give an exact sum rule equal to minus the total optical-square integral, with no assumed endpoint limits for the expansion. In Bianchi I, this optical saturation fixes the metric on the kernel of the conserved spatial covector. We classify the resulting geometry: a non-static metric has at most two saturated unoriented lines, corresponding to four oriented rays; two lines force diagonalizability by a constant spatial transformation, and a third forces staticity. Periodic and finite-duration geometries attain the bound. For finite pulses with a common static exterior, we derive the negative affine curvature integrals, their weak-amplitude angular dependence, and a nonperturbative bound on the metric excursion from three directional integral budgets. Saturated modes of a massless minimally coupled test scalar propagate without Bogoliubov mixing across the pulse. We also state the field-equation and averaged-energy assumptions under which these geometric results imply matter or semiclassical rigidity.