Cosmic solenoids: Minimal cross section and generalized flux quantization

A self-consistent general relativistic configuration describing a finite cross-section magnetic-flux tube is constructed. The cosmic solenoid is modeled by an elastic superconductive surface which separates the Melvin core from the surrounding flat conic structure. We show that a given amount (Formula presented) of magnetic flux cannot be confined within a cosmic solenoid of circumferential radius smaller than (Formula presented) without creating a conic singularity (the expression for the angular deficit is different from that naively expected). Gauss-Codazzi matching conditions are derived by means of a self-consistent action. The source term, representing the surface currents, is sandwiched between internal and external gravitational surface terms. Surface superconductivity is realized by means of a Higgs scalar minimally coupled to projective electromagnetism. Trading the “magnetic” London phase for a dual “electric” surface vector potential, the generalized quantization condition reads (Formula presented) with Q denoting some dual “electric” charge, thereby allowing for a nontrivial Aharonov-Bohm effect. Our conclusions persist for dilaton gravity provided the dilaton coupling is subcritical.