We include effects of self-gravitation in the self-interaction of single electrons with the vacuum electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the k-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 and equations of hydrostatic equilibrium to perform an exact calculation of the bare mass and electron radius. In the closed-form solution we find the electron radius to be   . is the Planck length , which is educed from first principles. The radius is independent of it depends on , and The elecron mass is in terms of the Planck mass . We find that the electromagnetic and gravitational fields merge at in terms of the Planck mass . Since the unified field is independent of (it depends on and alone) we conclude that it is continuous. We extend our result to calculate the pressure profile within the electron. We present both numerical, and analytical calculations based on approximations. We also calculate the speed of excitations within the electron which display two distinct regions; a hard shell surrounding a softer core. We also provide an explanation for the large discrepancy between the theoretical and measured mass of electrons.
PACS 04.62.+ v, 11.10.Gh, 12.10.-g, 12.20.Ds