Self-forces on electric and magnetic linear sources in the space-time of a cosmic string.

In this paper we calculate the magnetic and electric self-forces, induced by the conical structure of a cosmic string space-time, on a long straight wire which presents either a constant current or a linear charge density. We also show how these self-forces are related by a Lorentz tranformation and, in this way, explain what two different inertial observers detect in their respective frames. PACS numbers: 98.80.cq, 04.40.+c, 41.20.-q e-mail: [email protected] Present address: Present address: Blackett Laboratory School of Natural Sciences Imperial College Institute for Advanced Study London SW7 2BZ Princeton, NJ 08540 UK USA It is well known that the space-time produced by a thin, infinite, straight cosmic string, has no Newtonian potential [1] and cannot induce curvature (locally the curvature vanishes everywhere except at the source). However, there are some global non-trivial topological effects associated with this space-time which can be measured [2]. Recently, Linet [3] and Smith [4] have shown that a charged point particle placed in a static space-time, produced by an infinite straight cosmic string, becomes subjected to a finite repulsive electric self-force. This phenomenon is a consenquence of the distortion in the particle field caused by the lack of global flatness of this space-time. The purpose of this paper is to investigate how the self-force phenomenon manisfests in the magnetic case; i.e., we study what happens either to an electric current or to a linear charge distribution in the conical space-time produced by a cosmic string. Furthermore, we show that the respective selfforces are related by a Lorentz transformation (a boost along the direction of the string). In order to analyse this problem we shall adopt, for simplicity only, the case where the magnetic and electric sources are both infinite straight wires parallel to the cosmic string, which we assume lies along the z-axis. Before we start our calculation, we add that the analysis presented here can also be applied to some elastic solids which present a specific kind of linear defects named disclinations [5]. As shown by Katanaev and Volovich [6], the change in the topology of the elastic medium produced by this linear defect is the same as the one produced by a cosmic string in Minkowski spacetime. This similarity goes beyond topology: for some applications both kinds of defects can be treated using the same geometrical approach; i.e., their surrounding space-time can be described by similar geometrical points of view. In this approach, the line element in the section z=t=constant, is given by dl(2) = dr 2 + rdθ, (1)