Gravitational repulsion in sources of the Reissner–Nordström field

Abstract

A number of aspects of the phenomenon of gravitational repulsion in static sources of the Reissner–Nordström field are investigated. It is found that in the case of perfect fluid spheres there exists a close relation between this phenomenon and the Weyl curvature tensor. In fact, it is proved that such a source gives rise to gravitational repulsion only if the pure gravitational field energy inside the sphere is negative. It is also proved that although the gravitational repulsion always takes place in the interior of a perfect fluid charged sphere when its radius r0 is less than the ‘‘classical electron radius’’ re, this is not necessarily so either in the case of anisotropic charged spheres or if the net charge of the body is concentrated at its boundary only. It is shown that the phenomenon can also occur inside charged sources with r0>re. New sources of repulsive gravitation are constructed. They differ from others in the literature, since they neither satisfy the equation of state of ‘‘false vacuum’’ nor are their total gravitational masses entirely of electromagnetic origin. It is found that the charge contributes negatively to the effective gravitational mass MG, in the sense that an increase in the charge causes a decrease in MG. The gravitational repulsion in the new models constructed here is explained as due to this negative contribution rather than due to the strain of vacuum because of vacuum polarization.