Null Energy Condition in Dynamic Wormholes

We extend previous proofs that violations of the null energy condition are a generic and universal feature of traversable wormholes to completely nonsymmetric time-dependent wormholes. We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and we do not have to make any technical assumptions about asymptotic flatness or other global properties. A key aspect of the analysis is the demonstration that time-dependent wormholes have two throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole.