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 geometry 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 electric flux determined by the global topology, which is proportional to the charge of the source, and is characteristic of the asymptotically flat cylindrical wormholes regardless of the details of the throat geometry.

About the traversability of thin-shell wormholes

“…As a final note, we should stress that the traversability analysis of the present work can also be carried out for topologically trivial configurations with shells separating inner from outer regions (see for instance [12][13][14][15]), as well as for multi-layer distributions in cylindrical spacetimes (see for example Refs. [16][17][18]).…”