Narrow Results

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.