Conductors and superconductors in stationary spacetimes: generalized Schiff-Barnhill and Meissner effects
Previous studies on conductors and superconductors in curved spacetimes, and the gravitationally-induced electric and magnetic fields in them, are mostly restricted to the limit of weak fields and low velocities. Also the observer-dependence of these phenomena are not discussed in the literature. In this article, following London's phenomenological approach to superconductivity, we consider the electrodynamics of superconductors in stationary spacetimes without employing any weak field or low velocity limit. To this end, first we define the 3-force acting on charged particles in gravitational and electromagnetic fields, and derive its explicit form in a general spacetime decomposition formalism. Then, to highlight the role of observers, we apply the force equation to the free charges in superconductors in stationary spacetimes in the two well known threading and slicing decomposition formalisms. Applying the stationary condition in the superconducting state, we arrive at the generalized Schiff-Barnhill and Meissner effects, which compared to the low velocity and weak field limit include extra terms originating from the recently introduced gravitationally-induced constitutive equations. To show the consistency of our approach, we also derive the generalized Meissner effect from the second London equation in stationary spacetimes.