A Global Solution of the Einstein-Maxwell Field Equations for Rotating Charged Matter

Abstract

A stationary axially symmetric exterior electrovacuum solution of the Einstein-Maxwell field equations was obtained. An interior solution for rotating charged dust with vanishing Lorentz force was also obtained. The two spacetimes are separated by a boundary which is a surface layer with surface stress-energy tensor and surface electric 4-current. The layer is the spherical surface bounding the charged matter. It was further shown, that all the exterior physical quantities vanished at the asymptotic spatial infinity where spacetime was shown to be flat. There are two different sets of junction conditions: the electromagnetic junction conditions, which were expressed in the traditional 3-dimensional form of classical electromagnetic theory; and the considerably more complicated gravitational junction conditions. It was shown that both—the electromagnetic and gravitational junction conditions—were satisfied. The mass, charge and angular momentum were determined from the metric. Exact analytical formulae for the dipole moment and gyromagnetic ratio were also derived. The conditions, under which the latter formulae gave Blackett’s empirical result for rotating stars, were investigated

The Angular Momenta, Dipole Moments and Gyromagnetic Ratios of the Neutron and the Muon

“…We have obtained the dipole moments angular momenta and gyromagnetic ratios of the neutron and the muon using the analytical formulae developed in [1]. The values found, are consistent with the expected values of these quantities.…”

“…In accordance with the results of [1], the dipole moment n P , total angular momentum n J and gyromagnetic ratio n n P J are ( )…”

“…We shall express the Electromagnetic Field Equations in terms of the 3-vectors representing the electric and magnetic intensities and the corresponding inductions E, H, D, B as follows: For the details of how these expressions are derived, see [1].…”

“…The mass of the neutron, its classical radius, the square of the classical radius, and the vacuum speed of light, are Associated with n m there is an electric charge n m G whose numerical value is given by the first of equations (2) above [1]. If there is an additional charge q then the total electric charge will be + n m G q esu .…”

“…The purpose of this note is to derive analytical formulae for the dipole moments, angular momenta and gyromagnetic ratios of the neutron and the muon. The background to this work is fully explained in reference [1] and a parallel paper on the electron and neutron [2] follows the same methods as presented here.…”