Gravitation and magnetic charge

Abstract

Based on the static spherically symmetric solutions of the generalized theory of gravitation it is found that electric and magnetic charges are two fundamental constants of integration and that the corresponding electric, magnetic, and gravitational fields are regular everywhere only if the magnetic charge $\mathfrak{g}\ensuremath{\ne}0(\ensuremath{\sim}{10}^{18}e)$. The magnetic charge $\mathfrak{g}$ assumes an infinite spectrum of values and is an invertible function of mass. For magnetic charge $\mathfrak{g}=0$, the solutions reduce to the Nordstr\"om solution of general relativity in the limit of large $r$. The theory leads to elementary particles of finite self-energy [$\ensuremath{\Delta}(\ifmmode\pm\else\textpm\fi{}E)=m{c}^{2}\ensuremath{-}\frac{{(2{\mathfrak{g}}_{0})}^{2}}{{l}_{0}}$] and binding energy. The structure of an elementary particle which is due to the existence of finite $\ifmmode\pm\else\textpm\fi{}\mathfrak{g}$ consists of a magnetically neutral core of matter containing a distribution of magnetic charge density in stratified layers of sharply decreasing magnitude and alternating signs so that magnetic monopoles associated with a long-range field do not exist. As a consequence of the general covariance of the theory the surfaces of zero magnetic charge density in the particle core have an indeterminacy. These facts lead to a mass spectrum for elementary particles. In addition to charged electric and magnetic currents, the theory yields an electrically neutral current and the corresponding fields. The neutral current and the corresponding neutral field are the classical counterparts of the vacuum polarization in quantum electrodynamics. For every positive-energy solution there exists also a negative-energy solution with the corresponding electric charge. For $\mathfrak{g}=0$, the volume integral of the neutral current density diverges. The asymmetry of Maxwell's equations with regard to the absence of a magnetic current can be understood because the neutral and charged magnetic currents and the neutral part of the electric current are localized in the core of the elementary particle. Furthermore, the theory yields two lengths of the dimensions of ${10}^{\ensuremath{-}25}$ and ${10}^{\ensuremath{-}15}$ cm which could serve to differentiate between leptonic and hadronic processes. The presence of negative-energy solutions along with positive-energy solutions points to a large-scale symmetry with respect to a distribution of matter and antimatter in the universe.