Geometrization of classical fields in the embedded spaces model

The paper shows that the joint nonconfigurational geometrization of the gravitational and electromagnetic elds leads to a metric manifold related to the Model of Embedded Spaces (MES). MES assumes the existence of an eigen manifold of a massive particle (an element of distributed matter) and states that the space-time of the Universe is the 4d-metric result of dynamic embedding of such manifolds, whose partial contribution is determined by matter interactions. An embedding can be equipped with a Riemann-like geometry, whose di erential formalism in the test particle approximation is obtained by a formal generalization of the gradient operator. The paper continues the work on the substantiation of the dynamic embedding geometry and the geodesic equation is derived. In the applied part of the study, the MES-analogue of the Maxwell equation is obtained and the derivation of the MES-analogue of the Einstein equation is corrected. Some fundamental physical and cosmological consequences of the developed concept are discussed.