Cosmic Solenoids: Minimal Cross-Section and Generalized Flux Quantization

Abstract

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 $Φ$ of magnetic flux cannot be confined within a cosmic solenoid of circumferential radius smaller than $\frac{\sqrt{3G}}{2πc^2}Φ$ without creating a conic singularity. 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: $e/{hc} Φ+ 1/e Q=n$ with $Q$ denoting some dual 'electric' charge, thereby allowing for a non-trivial Aharonov-Bohm effect. Our conclusions persist for dilaton gravity provided the dilaton coupling is sub-critical.

Revtex, 11 twocolumn pages, 3 eps figures (accepted for publication in Phys. Rev. D)