Electromagnetic field bumps: Electro-gravitational models of the classical electron and dark energy

Abstract

Previously we conjectured that extremely high Electromagnetic (EM) fields in a vacuum generate a gravitational field that causes Maxwell's equations to no longer be linear. This results in a "4-force" in the field configuration space, also called "four-current density". Based on the 4-current density, we postulate that the electric charge is the result of a high EM field. Considering the electrostatic potential with central symmetry and with the assumption that it cannot exceed the Planck potential, we show that the associated electric charge is confined inside a sphere with non-zero radius, centered at the origin. We propose to represent this elementary charge e, thus replacing the point electron of the standard model with a "bump" of the EM field. According to this model, the gravitational field created by EM is repulsive up to the classical radius of the electron, then attractive beyond. This property provides a model for dark energy, which is believed to cause the accelerated expansion of the universe and whose nature is unknown today. We thus replace the cosmological constant of the standard model {\Lambda}CDM by a "field of EM bumps".