LAUSR

Abstract It is shown in the tetrad representation that there are Reissner–Nordström solutions describing systems with a finite action and total inertial mass equal to the gravitational mass. These systems consist of entirely electromagnetic and gravitational fields. There are not any massive point-charges inside them. The system is called ‘‘the classical electron’’ if its charge is equal to $${-}4.80\times 10^{-10}$$ esu. Its electromagnetic field is localized in a space region of about $$10^{-34}$$ cm. The total stress tensor for the classical electron is shown to be identically zero. This means that there is no need in an additional surface-tension of unknown nature preventing the system disintegration, as it takes place in the Lorentz electron model. The hypothesis that gravitation can play a crucial role in the structure of all elementary particles is discussed.