Gravitational sources of purely electromagnetic origin

Abstract

The Einstein-Maxwell field equations for charged dust corresponding to static axially-symmetric metric of Levi-Civita have been studied. It has been shown that when the metric potentialsgij are functions of only one of the coordinates, viz.,r, the interior charged dust becomes purely of electromagnetic origin, in the sense that the physical quantities like the energy density, the effective gravitational mass, etc., are dependent only on the charge density and vanish when this charge density vanishes. Such models are known as electromagnetic mass models in the classical electrodynamics. An interior charged dust solution corresponding to this case has been obtained which, in a sense, represents an infinite dust distribution of electromagnetic origin. In the second case, viz., when the metric potentials are functions of the coordinatesr andz both, it has been shown that some of the situations correspond to electromagnetic mass models. An example to illustrate this case has been obtained. This represents the source of the ‘Reissner-Nordstrom-Curzon’ field (an analogue of the Reissner-Nordstrom solution obtained by Curzon) which according to Curzon describes the exterior field of an electron.