How current loops and solenoids curve spacetime

The curved spacetime around current loops and solenoids carrying arbitrarily large steady electric currents is obtained from the numerical resolution of the coupled Einstein-Maxwell equations in cylindrical symmetry. The artificial gravitational field associated to the generation of a magnetic field produces gravitational redshift of photons and deviation of light. Null geodesics in the curved spacetime of current loops and solenoids are also presented. We finally propose an experimental setup achievable with current technology of superconducting coils, that produces a phase shift of light of the same order of magnitude as astrophysical signals in ground-based gravitational wave observatories.