A Five-Dimensional Model of the Gravitational Interaction of an Electromagnetic Field in an Affine-Metric Space

A geometric model for the gravitational interaction of an electromagnetic field in an affine-metric space with torsion and nonmetricity is proposed which describes the dynamics of an empty 5-dimensional affine-metric space. The gravitational and the electromagnetic field are presented in terms of the metric tensor of a 5-dimensional space-time. The equations of the theory are deduced from the variation principle with the use of the (4 + 1)-splitting formalism. Exact spherically symmetrical solutions have been obtained for the system of equations of the presented theory, and their possible astrophysical consequences have been investigated.