Mathematics – Logic
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14.1167v&link_type=abstract
General Relativity and Gravitation, vol. 14, Dec. 1982, p. 1167-1181.
Mathematics
Logic
4
Electromagnetism, Gravitation Theory, Unified Field Theory, Cosmology, Electromagnetic Fields, Mathematical Models, Scalars, Universe
Scientific paper
A version of the five-dimensional unified theory of gravitation, electromanetism, and scalar field is elaborated. It is shown that in this theory the principal features of Kaluza's five-dimensional theory and the Weyl one, based on non-Riemannian geometry and on conformal mapping, are combined. Reasons are adduced for choosing the physical 4-metric to be conformal to the 4-metric obtained by 1 + 4 splitting of the initial five-dimensional manifold. The electrical charge and current are shown to appear in the geometrical theory if the condition of cylindrical symmetry in the fifth coordinate is substituted by the condition of quasi-cylindrical symmetry; that is, the physical 4-metric and the vector potential of electromagnetic field remain independent of the fifth coordinate, while the scalar field depends on it. Two kinds of the most important exact solutions to the 15 field equations are treated, namely static spherically symmetrical solutions and homogeneous isotropic cosmological models.
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