Pointlike Electric Charge in Gravitational Field Theory

Abstract

The existence of charged elementary ’point particles’ still is a basically unsolved puzzle in theoretical physics.The present work takes a fresh look at the problem by including gravity—without resorting to string theory. Using Einstein’s equations for the gravitational fields in a general static isotropic metric with the full energymomentum tensor (for the charged material mass and the electromagnetic fields) as the source term, a novel exact solution with a well-defined characteristic radius emerges where mass and charge accumulate:—with being the ’classical’ radius associated with the total charge and where is the Schwarzschild radius belonging to the observable mass (for the electron one has m and m). The resulting ’Einstein-Maxwell’ gravitational electron radius can also be written as , where m is the fundamental Planck length and the fine-structure constant, which yields m