The external gravitational and electromagnetic fields of rotating bodies

Abstract

In previous papers (1941, 1947) the author has shown that the loss of gravitational energy of a rotating system such as a rod may be established by considering the non-periodic terms of order I 2 ω 5 / r 3 in the equation G μ v = 0 for the external field, I being the moment of inertia in the case of a rod. The present investigation begins by calculating the terms of order l 2 ω 6 / r 2 in the expressions for G μ v . It is found that the equation G μ v = 0 has no solution. Values of the g μ v can be determined, however, for which the material energy-tensor has the form of the Faraday-Maxwell stress-tensor due to certain periodic electromagnetic fields. In this way a link is established between periodic gravitational and electromagnetic fields, but the electromagnetic field is not uniquely determined by the analysis. Next a rotating sphere is considered. The calculation is carried out as far as terms of order m 3 ω 2 / r 7 in the G μ v . Again it is found impossible to find a solution of the equation G μ v = 0, but the ‘material’ energy-tensor can be identified with an electromagnetic energy-tensor. In both the cases of the periodic system and of the sphere potentials are found for which the energy-tensor represents a field of the form proposed by Blackett (1947), but the investigation does not rule out the possibility that other alternative solutions may exist. The solution in the case of a ‘Blackett field’ requires a current-charge vector inside the material with a non-zero charge, but the precise values of either the charge or current densities are determined. The solution, in fact, covers the case of a rotating charge as well as of a rotating ‘neutral' body. Presumably, further physical considerations must be taken into account to solve the problem completely. As the rotation of the earth produces no visible electric field, the resultant charge must be small.