Maxwell equations in curved space-time: non-vanishing magnetic field in pure electrostatic systems

Solutions of the Maxwell equations for electrostatic systems with manifestly vanishing electric currents in the curved space-time for stationary metrics are shown to exhibit a non-vanishing magnetic field of pure geometric origin. In contrast to the conventional magnetic field of the Earth it can not be screened away by a magnetic shielding. As an example of practical significance we treat electrostatic systems at rest on the rotating Earth and derive the relevant geometric magnetic field. We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings.