Cosmic Solenoids: Minimal Cross-Section and Generalized Flux Quantization

On dimensional grounds, however, it is clear that a string is not really capable of fully representing the case of an arbitrarily narrow tube. In particular, the innocent looking magnetic flux string configuration eq.(1) is apparently sourceless. To keep track of the source, one should consider a magnetic flux tube of finite radius, and let a surface current constitute the source. This way, to keep the total magnetic flux finite, the surface current gets infinitely large as the tube becomes infinitesimally narrow. The situation is conceptually and drastically changed once gravity (or string theory) enters the game. In this paper, a self-consistent general relativistic configuration describing a finite cross-section cosmic solenoid is constructed. The cosmic solenoid is modeled by an elastic superconductive surface which separates the curved inner core from the surrounding flat conic structure. Any attempt to squeeze the cosmic solenoid, while holding its total magnetic flux Φ fixed, comes with a cosmic penalty. In the extreme, if trying to imprison any given amount of magnetic flux within a tube of a sub-critical cross-section, one pays the ultimate price of closing the surrounding space and creating a conic singularity. Adopting the h̄ = c = 1 units, here are some exact spacetime configurations [3] relevant to our discussion: • The general stationary cylindrically symmetric vacuum solution of Einstein equations is given by