Wormholes with arbitrarily small amounts of exotic matter: a critique

Quantum inequality (QI) bounds have been used to place severe restrictions on "designer spacetimes", such as traversable wormholes and warp drives. Most of the QI bounds which have been proven to date involve averages of the energy density in some observer's frame, over his worldline. In the current work, a QI bound on the expectation value of the null-contracted stress tensor, averaged over a timelike worldline, is used to obtain constraints on the geometries of traversable wormholes. In the present context, this type of QI bound has certain advantages over the previous QIs. Particular attention is given to the wormhole models of Visser, Kar, and Dadhich (VKD) and to those of Kuhfittig. These are models which use arbitrarily small amounts of exotic matter for wormhole maintenance. We show that macroscopic VKD models are either ruled out or severely constrained by the QI bound. A recent model of Kuhfittig is shown to be, despite claims to the contrary, non-traversable.