Traversable Kaluza-Klein wormholes?

Abstract

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.