Explicit Solutions of Maxwell-Einstein Equations

Abstract

This article concerns the effect of gravitation field of the spherical electro-magnetic wave (EMW) on its propagation in vacuum. For this it was received a solution of the coupled Maxwell-Einstein equations. It is shown that in addition with traveling wave EMW at а great distance some new solution of so-called instanton type exists. It describes the process of quantum tunneling between degenerate states corresponding to convergent and divergent spherical waves in quasi-classical approximation. It is shown that these solutions for zero moment momentum describe fields of point-like charges - electric e and magnetic g. Symmetry of Maxwell equations with respect to group U(1) of dual transformations: (E+iH) → (E+iH)e iα , (E and H are electric and magnetic fields, α - is real parameter) is valid for generalized charge e + ig, which is transformed in the same manner. Spontaneous breaking of symmetry of this group, which is characterized tgα = - g/e, leads to arising mass-less particles (photons?) due to Goldstone theorem. This also leads to the fact that magnetic charges cannot be detected in Nature.