  We provide the detailed calculation of a general form for Maxwell and London
equations that takes into account gravitational corrections in linear
approximation. We determine the possible alteration of a static gravitational
field in a superconductor making use of the time-dependent Ginzburg-Landau
equations, providing also an analytic solution in the weak field condition.
Finally, we compare the behavior of a high-Tc superconductor with a classical
low-Tc superconductor, analyzing the values of the parameters that can enhance
the reduction of the gravitational field.
