# Black hole in a superconducting plasma

## TL;DR

This paper explores how superconducting plasma states behave near black hole horizons, revealing that under certain conditions, magnetic fields are expelled and the plasma acts as a superconductor, regardless of black hole spin.

## Contribution

It extends the generalized vortical formalism to curved spacetime, showing magnetic field expulsion and superconducting behavior at black hole horizons in various geometries.

## Key findings

- Magnetic field is expelled from the black hole horizon under symmetric conditions.
- Plasma near the horizon behaves as a perfect superconductor.
- Results hold for both rotating and nonrotating black holes.

## Abstract

The generalized vortical formalism provides an electrodynamic description for superconducting states---in the generalized vortical formalism, a superconducting state may be defined by the vanishing of an appropriate generalized vorticity and characterized by zero generalized helicity for incompressible fluids. In this article, we investigate these states for compressible plasmas in black hole spacetime geometries using the curved spacetime generalization of the grand generalized vortical formalism. If the magnetic field is axisymmetric and the thermodynamic properties are symmetric about the equatorial plane, the resulting states are characterized by a vanishing skin depth and a complete expulsion of the magnetic field at the equator of the black hole horizon. Moreover, if the thermodynamic properties of the plasma are uniform at the horizon, we find that the magnetic field is completely expelled from the horizon, and the plasma behaves as a perfect superconductor near the horizon. This result is independent of the spin of a black hole, holding even for a (nonrotating) Schwarzschild black hole, and demonstrates that the geometry near black hole horizons can have a significant effect on the electrodynamics of surrounding plasmas.