Traversability as a Control-Limited Dynamical Phase

Traversability in wormhole and near-horizon spacetimes is conventionally treated as a static geometric property tied to topology or sustained violations of classical energy conditions. This work proposes an alternative, information-first formulation in which traversability is defined operationally as a transient, control-limited dynamical phase of null congruence evolution.

Starting from the Raychaudhuri equation, we separate baseline geometric focusing from bounded, localized defocusing authority modeled as an admissible control input with finite response latency. Accessibility is defined as the existence of a finite affine-parameter interval during which congruence expansion remains nonnegative, preventing caustic formation. This leads to an operational focusing-surplus functional and a single inequality governing accessibility.

In dimensionless form, a universal kinematic floor emerges: below a minimum duration �, resealing is unavoidable under any bounded delayed control. Incorporating near-horizon redshift yields a practical dilation tax, whereby modest proper-time control near the bottleneck corresponds to arbitrarily large coordinate-time cost for distant observers. The framework induces a natural phase structure (Sealed / Marginal / Open) and predicts that transient accessibility events (“causal knocks”) are generic, while persistent echo trains require sustained control authority and are therefore non-generic.

Semiclassical traversable wormholes, double-trace deformations, negative-energy shocks, and analog horizon models are interpreted as distinct realizations of the same control-limited inequality rather than fundamentally separate mechanisms. The results reframe traversability as a regulated dynamical phenomenon governed by control authority, delay, and duration, rather than a static geometric classification.