0 Electrostatic in Reissner - Nordström space - time with a conical defect

It is well known that the gravitational field modifies the electrostatic interaction of a charged particle in such a way that the particle experiences a finite self-force [1,2]. The origin of this force comes from the space-time curvature associated with the gravitational field. On the other hand, even in the absence of curvature, such as in the conical space-time of an infinite straight cosmic string [3], it was shown that a charged point particle [4] or a linear charge distribution [5] placed at rest in this background becomes subject to a finite repulsive electrostatic self-force. In this case, the origin of this force is the distortion in the particle field caused by the lack of global flatness of the space-time of a cosmic string. Therefore, the modifications of the electrostatic potential comes from two contributions, one of geometric origin and the other of topological one. Some authors have suggested that the most simple exact solutions of Einstein’s equations can easily be generalized to include a conical defect [6]. Such space-times have been considered in different context and some investigations were done in these backgrounds [7]. In this paper we determine the expression for the electrostatic potential generated by a point charge held stationary in the space-time of ReissnerNordström pierced by a cosmic string and also determine the self-energy. These results extend previous one obtained by Linet [8] in the case of a Schwarzschild background with conical defect. The Reissner-Nordström space-time endowed with a conical defect takes the following