M, S. Dmytriiev, V. D. Gladush


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

Ключові слова

five-dimensional space-time; Kaluza-Klein model; time-dependent solution; black hole model; cosmological model

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Bronnikov K.A., Rubin S.G.:2008, Lectures on Gravity and Cosmology, Moscow, Moscow Engineering Physics Institute, 2008, 460 pp.(in Russian)

V.D.Gladush, Nadim Al-Shawaf: 2015, Odessa Astron. Publ., 2, 28.

Hongya Liu et al.: 1993, J. Math. Phys., 34, 9.

Gladush V.D.: 1979, Sov. Phys. J., 22, 11, 1172.

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