Model for Classical Electron with Finite Mass and Action

Abstract

It is shown in the tetrad representation that there are Reissner--Nordstr\"om solutions with a finite action and total inertial mass equal to the gravitational mass of the considered system. These solutions describe systems of electromagnetic and gravitational fields without any admixture of massive point-charges. The stress tensor for this solutions is shown to be identically zero. This means that there is no need in additional nonelectromagnetic surface-tension, existing in the Lorentz electron model, preventing the system disintegration. The hypothesis that gravitation can play a crucial role in the structure of elementary particles is discussed.