Josephson Effects in Slowly Rotating Spacetimes

TL;DR

This paper analyzes how slow rotation in spacetime influences Josephson effects, distinguishing between gravitational redshift and frame dragging, and provides a framework for superconducting circuits in such spacetimes.

Contribution

It offers a covariant, gauge-invariant formulation of Josephson phenomena in slowly rotating spacetimes, clarifying the effects of rotation and redshift on Josephson relations and interferometry.

Findings

Redshift effects on Josephson frequencies remain unchanged at linear order in rotation.

AC Josephson relation retains its redshifted form with proper voltages.

DC critical current at infinity is unaffected by linear-order rotation without azimuthal condensate momentum.

Abstract

We investigate Josephson phenomena in a slowly rotating stationary spacetime, emphasizing the distinct roles of gravitational redshift and rotational frame dragging motivated by [10.1007/JHEP02(2026)006]. Using a covariant formulation based on gauge-invariant phase dynamics and conserved currents within a $3+1$ decomposition, we analyze both AC and DC Josephson effects and interferometric configurations. Restricting attention to linear order in the rotation parameter $a$, and working in the Eulerian/ZAMO frame, we show that in the slow-rotation slicing adopted here the lapse function agrees with its static (Schwarzschild-type) form up to $\mathcal{O}(a^2)$, while rotational effects enter through the shift vector. Consequently, redshift effects on Josephson frequencies and DC critical currents remain unchanged relative to the non-rotating case at $\mathcal{O}(a)$. The AC Josephson relation retains its redshifted structure when expressed in terms of proper voltages and reduces to the standard flat-spacetime form when formulated in terms of asymptotic (Killing-time) observables. Likewise, the DC critical current measured at infinity scales with a single power of the lapse function and is unaffected by rotation at linear order in the absence of azimuthal condensate momentum. Rotational effects become relevant only in configurations sensitive to spatial phase transport or to synchronization with respect to the global time coordinate. In particular, RF-driven interferometric setups can acquire Sagnac-type phase offsets associated with frame dragging, whereas the DC fluxoid constraint remains unshifted at linear order in the present approximation. Our results provide a clean separation between lapse-driven redshift effects and shift-driven rotational contributions in Josephson physics and furnish a consistent framework for superconducting circuits in stationary spacetimes.