Exact axially symmetric stationary solutions of the Kaluza-Klein-Jordan-Thiry theory

Exact axially symmetric solutions of the Kaluza-Klein-Jordan-Thiry five-dimensional theory are obtained and studied. These metrics represent the exterior gravitational, electromagnetic, and scalar fields of systems that are characterized by having inertial and gravitational masses, electric charge, magnetic charge, angular momentum, and deformations from spherical symmetry, even in the absence of rotation. These conserved quantities are explicitly expressed in terms of the parameters of the metric, and they are also, formally, given as volume integrals of a hypothetical energy-momentum tensor that represents interior matter fields. The spherically symmetric solutions of Chodos and Detweiler, and the magnetic monopoles of Gross, Perry, and Sorkin are included as special cases. Mass-charge relations are found for the asymptotically flat metrics with zero magnetic charge, which suggest that these metrics do not describe fields of known elementary particles, but could represent macroscopic configurations.