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 ${{\kappa }^p}_q$. 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 ${{\kappa }^p}_p=\kappa <0$ (ordinary matter) and attracted toward the shell if $\kappa >0$ (exotic matter). The total image charge is zero for exterior problems, while for interior problems $Q/q=-\kappa r_e$, 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 $Q_{\mp }^{wh}/q=-1/({\kappa }_{wh}{r}_{\pm })$.

(15 pages, 6 figures; the work had been extended, corrected and reformulated from version v1 to v2, and minor misprints corrected from v2 to v3)

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• Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes
• Arbitrarily coupled massive scalar field in conical thin-shell spacetimes
• About the traversability of thin-shell wormholes