2014/08/20 by H. Dekker, Dekker, H.
Physics and Astronomy · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1408.4796
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 energy-momentum 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: r\rm c=√r\rm ero/2---with r\rm e=Q2 /4πεomc2 being the 'classical' radius associated with the total charge Q and where ro=2mG/c2 is the Schwarzschild radius belonging to the observable mass m (for the electron one has r\rm e≈10-15m and ro≈ 10-57m). The resulting 'Einstein-Maxwell' gravitational electron radius can also be written as r\rm c=ℓ\rm P√α\rm e, where ℓ\rm P=√(ℏ G/c3)≈10-35m is the fundamental Planck length and α\rm e=e2 /4πεoℏ c≈1/137 the fine-structure constant, which yields r\rm c\rm electron=1.38063×10-36m.