Cosmic Solenoids: Minimal Cross-Section and Generalized Flux Quantization

TL;DR

This paper models a finite cross-section magnetic flux tube, called a cosmic solenoid, in general relativity, revealing constraints on flux confinement, deriving matching conditions, and exploring generalized flux quantization with potential Aharonov-Bohm effects.

Contribution

It introduces a self-consistent relativistic model of cosmic solenoids with finite cross-section, including surface superconductivity and generalized flux quantization conditions.

Findings

A minimal radius for flux confinement without conic singularity.

Derivation of Gauss-Codazzi matching conditions for the flux tube.

Generalized flux quantization condition allowing for Aharonov-Bohm effects.

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 $\Phi$ of magnetic flux cannot be confined within a cosmic solenoid of circumferential radius smaller than $\frac{\sqrt{3G}}{2\pi c^2}\Phi$ 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: $e/{hc} \Phi + 1/e Q=n$ 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.