A superconductor pushes out a magnetic field like a sponge squeezing out water. This Meissner effect has been known for nearly a century, but it's usually calculated in a flat world — without gravity. In the strong field of a black hole or at enormous speeds, the picture changes.
The authors took the London equations and rewrote them for curved spacetime, without simplifying to weak fields. It turns out that even in a stationary superconductor, gravity generates an electric field — the Schiff–Barnhill effect. Under these new conditions, extra terms appear because the material itself responds to curvature.
The familiar Meissner effect is a special case. In a curved world, the magnetic field isn't expelled completely but with corrections that depend on gravity and velocity. This is a step toward understanding superconductivity in the most extreme places in the universe.
You can see the Meissner effect in a demonstration with a magnet levitating above a cooled superconductor, the magnet floats because the field is pushed out.
In Arthur C. Clarke's novel Rendezvous with Rama, superconducting shells protect the ship from external fields — in strong gravity, such technology would require new calculations.