Abstract
We consider wormhole solutions in five-dimensional Kaluza–Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the S3 part of a spacetime metric is the Hopf bundle S3 →S2 with fiber S1. We show that the fifth dimension spanned on the sphere S1 is compactified in the sense that asymptotically, at large distances from the throat, the size of S1 is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the four-dimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.