Electrostatics and self-force in asymptotically flat cylindrical wormholes

Abstract

The problem of the electrostatics in conical wormholes is revisited, now improving the background geometries with asymptotical flatness. The electric self-force on a point charge placed at different regions in the spacetime of a conical thin-shell wormhole connecting flat outer submanifolds is obtained and compared with the results of previous works. The study is also carried out in terms of a previously introduced analogy in which the effect of the matter shells on the electric field is reproduced by non-gravitating layers of charge located on the boundary surfaces. Besides, a better insight on the physical effects of a non trivial topology is obtained by means of a further analysis of the electric fluxes across the wormhole throat and at both spatial infinities. It is found that the throat is traversed by a non-arbitrary and finite topological flux, proportional to the charge of the source, which is characteristic of the asymptotically flat cylindrical wormholes regardless of the details of the throat geometry.