Electrostatic interaction of a pointlike charge with a wormhole

Abstract

A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only on the value and location of the charge, while the other, on the contrary, does not change when the charge is quasistatically moved. Correspondingly, the former is interpreted as being generated by the charge, and the latter as being source-free. It is shown that all source-free potentials differ in the flux through the throat (no "multipoles without multipoles"), which enables one to interpret the flux as the "charge" of the wormhole in agreement with Wheeler's concept of "charge without charge". The potential generated by the charge differs from Coulomb's and thus a force (called "self-force") acts on the charge even in the absence of the source-free field. This force is found explicitly in the limit of vanishing throat length. The result differs from that obtained recently by Khusnutdinov and Bakhmatov.

The published version: 1) the regularity is proven 2) the part is rewritten explaining where is the error in Khusnutdinov and Bakhmatov's result

References in corpus (4)

• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Might some gamma ray bursts be an observable signature of natural wormholes?
• Self force on charges in the spacetime of spherical shells
• Self-force of a point charge in the space-time of a symmetric wormhole

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• Self-force of a point charge in the space-time of a massive wormhole
• Self-force on a scalar point charge in the long throat
• Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
• Electrostatics in a simple wormhole revisited
• Response to the Comment on "Observing a wormhole"
• Electrostatics and self-force in asymptotically flat cylindrical wormholes
• Self-action in Gravity
• Scalar self-force on static charge in a long throat
• Self-force of a scalar charge in the space-time of extreme charged anti-dilatonic wormhole
• Renormalization for self-potential of a scalar charge in static space-times
• Bremstrahlung in wormhole spacetime with infinitely short throat