Superconducting cosmic strings. II. Spacetime curvature

We solve the Einstein-Maxwell and scalar field equations for an infinitely long bosonic superconducting cosmic string and explore the associated geometry of space-time. The metric describing the space-time is valid for both fermionic and bosonic superconducting cosmic strings. Due to general relativistic corrections, the magnetic field energy per unit length associated with the string does not diverge. A non-uniform charged Higgs field contribution to the stress-energy tensor endows the string with an effective mass that enables to attract gravitationally and alters its lensing properties.