Cosmic solenoids: Minimal cross section and generalized flux quantization - art. no. 045002

A self-consistent general relativistic configuration describing a finite cr oss-section magnetic-flux tube is constructed. The cosmic solenoid is model ed by an elastic superconductive surface which separates the Melvin core fr om the surrounding flat conic structure. We show that a given amount Phi of magnetic flux cannot be confined within a cosmic solenoid of circumferenti al radius smaller than (root 3G/2 pi c(2))Phi without creating a conic sing ularity (the expression for the angular deficit is different from that naiv ely 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. S urface superconductivity is realized by means of a Higgs scalar minimally c oupled to projective electromagnetism. Trading the "magnetic" London phase for a dual "electric" surface vector potential, the generalized quantizatio n condition reads (e/hc)Phi +(1/e)Q = n with Q denoting some dual ''electri c" charge, thereby allowing for a nontrivial Aharonov-Bohm effect. Our conc lusions persist for dilaton gravity provided the dilaton coupling is subcri tical. [S0556-2821(99)07610-9].