Auto-stabilized electron

Abstract

We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the [Formula: see text]-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius [Formula: see text]m, where [Formula: see text] is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at [Formula: see text] GeV in terms of the Planck mass [Formula: see text]. The unified field depends on [Formula: see text] and [Formula: see text] alone, independent of [Formula: see text]; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at [Formula: see text].