Constraints on Wormhole Geometries

A bound on negative energy densities in four-dimensional Minkowski spacetime was recently derived by Roman and Ford from quantum field theory. These quantum inequality restrictions constrain the magnitude and duration of the energy density seen by a timelike geodesic observer. The bound was applied to the stress-energy tensor of static traversable wormhole spacetimes, on a scale in which a local region of spacetime can be considered flat. The results imply that the existence of macroscopic traversable wormholes is very improbable. We analyse and discuss these results.