Internal structure of a classical spinning electron

Abstract

A classical model of the spinning electron in general relativity consisting of a rotating charge distribution with Poincaré stresses is set up. It is made out of a continuous superposition of thin charged shells with differential rotation. Each elementary shell is maintained in stationary equilibrium in the gravitational field created by the others. A class of interior solutions of the Kerr-Newman field is thus obtained. The corresponding stress-energy tensor naturally splits into the sum of two terms. The first one is the Maxwell tensor associated to a rotating charge distribution, and the second one corresponds to a material source having zero energy density everywhere, no radial pressure, and an isotropic transverse stress. These negative pressures or tensions are identified with the cohesive forces introduced by Poincaré to stabilize the Lorentz electron model. They are shown to be the source of a negative gravitational mass density and thereby of the violation of the energy conditions inside the electron.