Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

Abstract

The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a bulk field and a shell field. The bulk part corresponds to a field sourced by the test charge placed in a space-time without the shell. The shell field accounts for the discontinuity of the extrinsic curvature κ p q . An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge Q, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge q in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if κ p p = κ < 0 (ordinary matter) and attracted toward the shell if κ > 0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q = −κ r e , with r e the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found Q wh ∓ /q = −1/(κ wh r ± ).

Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes

“…Hence, for example, by studying the force on a static charged particle an observer could determine if the background is that of a gauge cosmic string or that of a thin-shell wormhole connecting two conical spacetimes. Also, in the case of topologically trivial spacetimes, an analogous analysis would allow to distinguish different interior geometries by studying the self-force on a charge placed at the exterior region beyond a matter shell [11,13,14]. The problem of the self-force on a scalar point charge appears as a natural but not at all trivial extension of previous work.…”

“…While the field equations of a given point source are locally those of Minkowski spacetime, the globally correct solution in a conical geometry is not symmetric around the source, and as a result a self-force appears on the charged particle [8]. Moreover, as shown in [9,10,11] for electrically charged point particles, the behavior of such force in relation with the position of the charge allows to distinguish between two locally identical geometries which differ in their global topological aspects. This provides a sort of tool for detecting wormholes of the thin-shell kind, whose geometries are locally the same of those of the type which they would connect [12].…”

Electrostatics and self-force in asymptotically flat cylindrical wormholes

“…Following this proposal, 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. Therefore, 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]. We will also consider an interpretation at the light of the analogy introduced in [15], where the effect of a cylindrical thin matter layer on the electric field is reproduced by replacing such shell by a suitablenon-gravitating -charge density placed at the corresponding boundary.…”

“…Therefore, 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]. We will also consider an interpretation at the light of the analogy introduced in [15], where the effect of a cylindrical thin matter layer on the electric field is reproduced by replacing such shell by a suitablenon-gravitating -charge density placed at the corresponding boundary.…”

“…We have then addressed the determination of the self-force in cylindrical thin-shell spacetimes [14,15] and also in spherically symmetric ones [16] or different number of spacetime dimensions [17]. Our program has also been extended to the case of scalar massless and massive fields [18,19].…”