# Superconducting fluctuation current in a space with the Kerr metric

## TL;DR

This paper investigates how a Kerr black hole's spacetime affects superconducting fluctuation currents in a ring, revealing shifts in transition temperature and temperature scale due to the black hole's gravitational effects.

## Contribution

It introduces a theoretical framework for analyzing superconducting fluctuations in extreme curved spacetime around a Kerr black hole.

## Key findings

- Kerr metric causes a shift in superconducting transition temperature.
- The temperature scale of superconductivity is altered by the black hole's spacetime.
- The fluctuation current exhibits unique features reflecting the Kerr black hole's properties.

## Abstract

We study a fluctuation current through a superconducting ring placed in a space with the Kerr metric. This attempt aims at exploring conceptual problem; namely, we are concerned with the question about the condensed state in an extreme space-time. The superconducting ring is supposed to be placed in the space surrounding the Kerr black hole (KBH) such that the rotating axis of the KBH penetrates the center of the ring. The formulation is based on the Landau-Ginzburg free energy functional of linear form. The resultant fluctuation current shows several peculiar features that reflect characteristic aspects of the KBH; that is, the effect of the Kerr metric gives rise to the shift of superconducting transition temperature as well as the scale change of absolute temperature.