Aharonov–Bohm Effect for Cooper Pairs in Kerr Spacetime: Gravitomagnetic Phase Shifts From Frame Dragging

ABSTRACT

The unification of quantum mechanics and general relativity remains a central problem in fundamental physics. Here, we study the gravitomagnetic Aharonov–Bohm (AB) effect for Cooper pairs in Kerr spacetime. Frame‐dragging by a rotating black hole (BH) generates an effective vector potential through the off‐diagonal metric term , coupling to the macroscopic phase of the superconducting condensate. We derive the gauge‐invariant phase shift for an interferometer with arms at radii and , where is the Cooper pair mass and the BH spin. The predicted phases reach radians for Sgr A* and for M87*. These are order‐of‐magnitude estimates of how the phase scales with mass, spin, and loop geometry, not a proposal to place superconducting rings near a BH, since the required circumferences are astrophysical. We show that tidal disruption of Cooper pairs is negligible for and connect the result to the geometric Berry phase. Our framework links quantum coherence to spacetime curvature and complements recent gravitational AB measurements in atom interferometry.