Wormholes and Flux Tubes in Kaluza-Klein Theory

In this work we investigate a class of spherically symmetric metrics in multidimensional (MD) gravity. The metric ansatz which is used has off diagonal elements which leads to these solutions having “electric” and/or “magnetic” charges. The solutions examined here are either MD wormholes or infinite/finite flux tubes. It is found that the type of solution obtained depends crucially on the relative magnitudes of these charges and thus on the form of the offdiagonal metric components. Usually in the discussion of wormhole or blackhole solutions such off-diagonal elements are not considered, (see for, example, [1][5]). The off-diagonal components of the MD metric play the role of gauge fields (U(1), SU(2) or SU(3) gauge fields), and a scalar field φ(x) which is connected with the linear size of the extra dimension. These geometrical fields can act as the source of the exotic matter necessary for the formation of the wormhole’s mouth. Such solutions were obtained in Refs. [6] [7] [8] [9]. These works indicate that the exotic matter necessary for the formation of the WH can appear in vacuum multidimensional gravity from the off-diagonal elements of the metric (the gauge fields) and from the G55 component of the metric (the scalar field), rather than coming from some externally given exotic matter. In Refs. [8], [9] a MD metric with only “electric” fields was investigated. In Ref [10] a MD metric with “magnetic” field = “electrical” field was investigated. In this paper we investigate the consequence of having both “electric” and “magnetic” Kaluza-Klein fields of varying relative strengths. We will consider 5D Kaluza-Klein theory as gravity on the principal bundle with U(1) fibre and 4D space as the base of this bundle [9].