Spherically symmetric T-solution of the equations of 5-dimensional Kaluza–Klein theory

Abstract

A geometrodynamical approach to the five-dimensional (5D) spherically symmetric cosmological model in the Kaluza–Klein theory is constructed. After dimensional reduction, the 5D Hilbert action is reduced to the Einstein form describing the gravitational, electromagnetic, and scalar interacting fields. The subsequent transition to the configuration space leads to the supermetric and the Einstein–Hamilton–Jacobi equation, with the help of which the trajectories in the configuration space are found. Then the evolutionary coordinate is restored, and the Cauchy problem is solved to find the time dependence of the metric and fields. The configuration corresponds to a cosmological model of the Kantovsky–Sachs type, which has a hypercylinder topology and includes scalar and electromagnetic fields with contact interaction.