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 $\Phi$ 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: $e/hc\Phi +1/eQ=n$ 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)

References in corpus (1)

• An Action for Black Hole Membranes

Cited by in corpus (7)

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• Static and Dynamic Melvin Universes
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• Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime
• Experimental test for extra dimensions in Kaluza-Klein gravity
• Properties of the magnetic universe with positive cosmological constant