A Semiclassical ANEC Constraint On Classical Traversable Lorentzian   Wormholes
  The present article lies at the interface between gravity, a highly nonlinear phenomenon, and quantum field theory. The nonlinear field equations of Einstein permit the theoretical existence of classical wormholes. One of the fundamental questions relates to the practical viability of such wormholes. One way to answer this question is to assess if the total \emph{volume} of exotic matter needed to maintain the wormhole is finite. Using this value as the lower bound, we propose a modified semiclassical volume Averaged Null Energy Condition (ANEC) constraint as a method of discarding many solutions as being possible self-consistent wormhole solutions of semiclassical gravity. The proposed constraint is consistent with known results. It turns out that a class of Morris-Thorne wormholes can be ruled out on the basis of this constraint. 
Kamal K. Nandi, Yuan-Zhong Zhang, and Nail G. Migranov