Superconductor in a weak static gravitational field

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-$$T_\text {c}$$ superconductor with a classical low-$$T_\text {c}$$ superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field