A geometrization of electric charge and mass by means of a solution to the Einstein and Maxwell equations for dust and a radial electric field

•Geometrization of dust and electromagnetic field in 4-space-time is implemented.•The given geometrization method differs from the method of string theory.•Discretization of wormhole space to a number of impenetrable cells is possible.•Mass excess is shown to be able to have the gravitational nature.•Pinch plasmoids generated in discharges can be explained gravitationally.

It has been shown that a physical system consisting of a free electromagnetic field and electrically neutral dust-like matter can be completely geometrized in 4-space-time. This system can be represented as worlds with a non-trivial topology, connected through an infinite set of the non-closing non-stationary wormholes. The geometric image of the electric charge turns out to be the non-closing static throat. The internal world of the charged particle is discretized into disconnected regions of space-time, impenetrable to light trajectories. The electric charge e, rest mass m0, and classical action of the gravitational field have a gravitational nature and are expressed in terms of the metric and the space-time curvature.