Model of Embedded Spaces: Gravitation and electricity

Abstract

Simultaneous non-configuration geometrization of classical electrodynamics and gravity leads to a 4D space which refer to the Model of Embedded Spaces (MES). MES presupposes the existence of their own space (manifold) in any massive particle (element of matter distribution) and argues that spacetime of the universe is the 4D metric result of dynamical embedding of proper manifolds, whose partial contribution is determined by matter interactions. The resulting space is equipped with Riemann-like geometry, whose differential formalism, in a test particle approximation, is obtained by a formal change of the gradient operator \(\partial /\partial {x^i} \to \partial /\partial {x^i} + 2{u^k}{\partial ^2}/\partial {x^{\left[ i \right.}}\partial {u^{\left. k \right]}}\), where uⁱ = dxⁱ/ds is the velocity of matter. In this paper the features of the geometry of dynamical embedding are analyzed, and MES analogs of the Einstein and Maxwell equations are obtained. It has been shown that the electric charge is a direct consequence of the gravitational constant and inertial mass of matter. We also discuss some fundamental physical and cosmological aspects of the developed ideas.