Ultramicro Black Holes and Finiteness of the Electromagnetic Contribution to the Electron Mass

Abstract

It is argued that the nonintegrably singular energy density of the electron's electromagnetic field (in both the classical point-charge model and quantum electrodynamics) must entail very strong self-gravitational effects, which, via black hole phenomena at finite radii, could well cut off the otherwise infinite electromagnetic contribution to the electron's mass. The general- relativistic equations for static, spherically symmetric stellar structure are specialized to treat the self-gravitational effects of static, spheri- cally symmetric, nonnegative, localized energy densities which may exhibit nonintegrable singularities at zero radius. It is demonstrated that in many situations, including the electromagnetic ones of interest here, such a system has a black hole whose Schwarzschild radius is that where the original energy per radial distance (the spherical shell area times the original energy density) reaches the inverse of (2G). The total mass of the system is that of this black hole (which follows in the usual way from its Schwarz- schild radius) plus the integrated original energy density outside this black hole. These results produce, for the classical point-charge model of the electron, an electrostatic contribution to its mass which is many orders of magnitude larger than its measured mass. For quantum electrodynamics, how- ever, the result is an electromagnetic mass contribution which is approxi- mately equal to its bare mass -- thus about half of its measured mass.