Corridor Shear in Military Training Airspace A Raychaudhuri-Inspired Test Framework Using the Arizona Range

The Raychaudhuri equation describes the evolution of bundles of nearby trajectories through expansion, shear, and rotation in spacetime. While originally formulated within General Relativity to describe geodesic congruences under gravitational curvature, the Raychaudhuri framework is fundamentally kinematic and can be applied more broadly to systems in which trajectories evolve through a structured environment. This paper proposes a corridor-shear hypothesis for repeatedly used military training airspace, using the Arizona restricted ranges as a natural observational laboratory. The hypothesis states that repeated high-performance aircraft maneuvers may generate persistent trajectory shear structures in airspace, forming corridors in which later anomalous aerial observations are more likely to occur. These corridors arise where aircraft traffic produces strong path overlap, directional mismatch, speed gradients, altitude transitions, and turning curvature. Three testable predictions follow. First, reported anomalous aerial phenomena should cluster spatially along historical maneuver corridors rather than appearing randomly across the training range. Second, the probability of such observations should increase shortly after periods of intense maneuver activity in the same corridor. Third, independent observations separated in time should recur along similar spatial pathways if corridor structures persist. To quantify these effects, the paper introduces a Corridor Shear Index (CSI) derived from aircraft trajectory data. The CSI measures memory-weighted conditioning of airspace based on local flight density, heading dispersion, velocity gradients, altitude transitions, and turning curvature. The central prediction is that the probability of anomalous observations correlates more strongly with CSI than with raw traffic density alone. Possible mechanisms for corridor formation include aerodynamic shear persistence, plasma or electromagnetic disturbances, atmospheric structures, or conditioning of a deeper space-phase medium. Regardless of the underlying mechanism, the Arizona training ranges provide a practical environment in which the corridor-shear hypothesis can be tested using flight-track archives and observation reports. The results of such tests could clarify whether anomalous aerial observations exhibit statistically significant correlations with historical maneuver corridors, thereby providing insight into the dynamical structure of repeatedly used airspace environments.