  The general principles needed to compute the effect of a stationary
gravitational field on the quasistationary electromagnetic phenomena in normal
conductors and superconductors are formulated from general relativistic point
of view. Generalization of the skin effect, that is the general relativistic
modification of the penetration depth (of the time-dependent magnetic field in
the conductor) due to its relativistic coupling to the gravitational field is
obtained. The effect of the gravitational field on the penetration and
coherence depths in superconductors is also studied. As an illustration of the
foregoing general results, we discuss their application to superconducting
systems in the outer core of neutron stars. The relevance of these effects to
electrodynamics of magnetized neutron stars has been shown.
