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

• Published in: The European physical journal. C, Particles and fields Vol. 76; no. 2; p. 1
• Main Author: Rubín de Celis, Emilio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 22.02.2016; Springer; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Elementary Particles; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory; Ordinary Matter; Exotic Matter; Cosmic String; Extrinsic Curvature; Equivalent Problem
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-016-3939-6

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 ∓ w h / q = - 1 / ( κ w h r ± ) .