Electromagnetic Field of Rotating Charged Bodies

The fact that the electromagnetic field of the Kerr-Newman solution of the Einstein-Maxwell equations is independent of the gravitational constant calls attention to and is illuminated by a problem of flat-space physics: the field of a rotating charged oblate ellipsoid of revolution of infinite conductivity and either (a) magnetic susceptibility of vacuum or (b) infinite magnetic susceptibility. These problems are solved for the case of interest, when the angular velocity is ω₀=a ̃ \~R^-2, where ̃ \~R²=R²+a², R and ̃ \~R being the semiminor and semimajor radii of the ellipsoid, respectively. It is shown that for small ω₀ the conductive surface current [case (a)] or the volume magnetization [case (b)] contributes to the total magnetic moment with twice the value of that generated by the convective current of the surface charge q. The multipole expansion of the fields F_μν [same for (a) and (b)] is obtained and shown to be formally identical to one of the generalized Deutsch solutions obtained in the Appendix. These are the exact solutions for the electromagnetic field of a rotating charged spherical perfect conductor with the magnetic susceptibility of the vacuum. Implications of these results for the understanding of properties of the Kerr-Newman black hole, such as the value 2 for the gyromagnetic factor, are analyzed.