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 $g_{t\varphi }$, coupling to the macroscopic phase of the superconducting condensate. We derive the gauge-invariant phase shift $\Delta \theta =(4\pi m^{\ast }Ma/\hslash )(1/r_2-1/r_1)$ for an interferometer with arms at radii $r_1$ and $r_2$, where $m^{\ast }=2m_e$ is the Cooper pair mass and $a$ the BH spin. The predicted phases reach $\left|\Delta \theta \right|\sim {10}^{24}$ radians for Sgr A* and $\sim {10}^{27}$ 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 $r\gtrsim 10r_s$ 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.