Electrostatics and self-force in asymptotically flat cylindrical wormholes

E Rubín De Celis,C Simeone

doi:10.1140/epjc/s10052-020-8063-y

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.

Highlights

Maxwell equations for curved spacetime [4] are: F μν √ −g = 4π j μ√−gFμν = Aν,μ − Aμ,ν jμ = a √q−a g δ(x − xa )
Taking into account the interesting results therein, in previous works we developed a program aimed to distinguish between topologically different geometries which are equal in the region where the charge is placed
When we compare the results with those previously obtained we can first note that in the exterior problem, we obtain a self-force towards the axis which qualitatively always reproduces the results shown in Fig. 4 of our previous work [14]

Summary

Introduction

Boundary conditions play a central role in the problem, as they explain the possibility of an anisotropic field around a rest point charge located in a region which is locally flat, and, the existence of an electric self-force in such an, at a first sight, trivial situation. Here we are interested in the problem of determining the electric field of a rest point charge in the background spacetime of a wormhole connecting two gauge cosmic string geometries at each side of the throat, joined to two Minkowski geometries in their corresponding outer regions. In the present work we will determine how this improvement in the kind of background geometries considered is reflected in the behavior of the electric self-force on a point charge, and how this compares with our previous results obtained for everywhere conical spacetimes [14,15]. Unlike what was pointed out in previous illuminating works on electrostatics in spherically symmetric wormhole spacetimes [12,13], here we show that the presence of a test electric charge fixes a finite flux traversing the cylindrical wormhole throat

The geometry

Field of a point charge

Evaluation of the self-force

Discussion