Quantum vacuum coupling still can't replace exotic matter in wormholes

Traversable wormholes require matter that violates the Null Energy Condition — a rule that normal matter cannot bend. Some proposals hoped that coupling matter to the vacuum energy might sidestep this requirement. Focusing on zero-tidal-force, static configurations, this work shows that the geometric "flare-out" condition a wormhole throat must satisfy is mathematically incompatible with any NEC-respecting source, regardless of how strongly matter and vacuum interact. The vacuum acts as a regulator that obstructs the required geometry rather than enabling it, reinforcing that classical energy conditions are not easily circumvented.