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 κpq . 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 κpp=κ0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q=−κre , with re 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 Qwh∓/q=−1/(κwhr±).