Traversable Kaluza–Klein Wormholes?

Various authors have suggested that Kaluza–Klein variants of traversable wormholes might to some extent ameliorate the defocussing properties (the curvature condition violations, and implied energy condition violations) inherent in positing the existence of a traversable wormhole throat. Unfortunately such a hope is ill-founded. We shall show that in a traditional Kaluza–Klein context the price paid for completely eliminating the defocussing properties of the wormhole throat is extremely high—to completely eliminate curvature condition violations the 5th dimension has to become truly enormous (formally infinite) in the vicinity of the wormhole throat, in a manner that is fundamentally incompatible with the traditional Kaluza–Klein ansatz. At best, the extra dimensions allow one to move the curvature condition violations around, they cannot be eliminated except at prohibitive cost. While traversable Kaluza–Klein wormholes might be interesting for other reasons, it must be emphasized that adding a 5th dimension is not particularly useful in terms of ameliorating violations of the curvature conditions.