The Equations of Codazzi and the Relations between Electromagnetism and Gravitation

Abstract

The aim of this paper is to show that, quite independently of any physical theory, the general equations of Codazzi on differential geometry lead to fundamental relations between the electromagnetic and the gravitational fields as soon as the external metric tensor of space-time is interpreted as an electromagnetic tensor. When the important special case of quasi static fields is considered, we get for a rotating body with no permanent magnetization: (1) The relation, previously studied by the author, between magnetic moment and angular momentum which explains the general features of stellar and terrestrial magnetism as well as the magnetic moment of the neutron; (2) a relation between gravitation and the electrostatic field, such that any massive body creates an electrostatic field by its own gravitation. The mean electrostatic fields of celestial bodies, including the earth, can be ascribed to this effect. When the gravitation produced by a given body is negligible (as in the laboratory) the equations of Codazzi show that the familiar Coulomb field is merely a consequence of the very rapid vibrations of the components ${g}_{4i}$ ($i=1,2,3$) of the internal metric tensor. Finally, for an uncharged body with permanent magnetization it can be shown that the curl of the ${g}_{4i}$ and the magnetic field are related as cause and effect.We think that these results are a confirmation of a fundamental result of our unified field theory: That the geometrization of electromagnetism must necessarily be achieved by the external metric of space-time.