T-SOLUTIONS OF THE 5D KALUZA-KLEIN MODEL

Abstract

We consider spherically-symmetric solution of the 5D Kaluza-Klein theory, which metric coefficients depend on time only. When we construct the appropriate 4+1 splitting of the five-dimensional space and then perform the conformal transformation we get the cosmological model with hypercylinder topology. There are scalar and electromagnetic fields with contact interaction. Besides this, these fields correspond to the inner region of the black hole in the appropriate choice of integration constants. Using 2+2+1 splitting technics and reduction we get the lagrangian of the model. After that we build the canonical formalism of the theory, which admits constraints. These are Hamilton, momentum and Gauss constraints. Momentum constraint is satisfied trivially in the homogeneous case. From the Hamilton constraint we obtain the Einstein-Hamilton-Jacobi equation. Main puprpose of this work is to investigate this equation and three types of models, which we get from it. It turns out that the configurations with removable and unremovable electric field are possible to exist in this case [Gladush et al., 2015]. Removable electric field can be eliminated with 5D coordinate transformation.