On Beltrami states near black hole event horizon

TL;DR

This paper investigates Beltrami plasma equilibria near spinning black hole horizons, deriving magnetic field profiles and conditions for magnetic field expulsion, with implications for black hole magnetosphere physics.

Contribution

It develops a framework for constructing magnetic field profiles in near-horizon plasmas, generalizing previous results to include non-zero vorticity and thermal effects.

Findings

Horizon magnetic field profiles satisfy coupled ODEs depending on boundary conditions.

Superconducting plasma states have boundary-condition-independent horizon profiles.

Two distinct length scales govern magnetic field variation and Beltrami term strength.

Abstract

In this article, we study Beltrami equilibria for plasmas in near the horizon of a spinning black hole, and develop a framework for constructing the magnetic field profile in the near horizon limit for Clebsch flows in the single-fluid approximation. We find that the horizon profile for the magnetic field is shown to satisfy a system of first-order coupled ODEs dependent on a boundary condition for the magnetic field. For states in which the generalized vorticity vanishes (the generalized `superconducting' plasma state), the horizon profile becomes independent of the boundary condition, and depend only on the thermal properties of the plasma. Our analysis makes use of the full form for the time-independent Ampere's law in the 3+1 formalism, generalizing earlier conclusions for the case of vanishing vorticity, namely the complete magnetic field expulsion near the equator of an axisymmetric black horizon assuming that the thermal properties of the plasma are symmetric about the equatorial plane. For the general case, we find and discuss additional conditions required for the expulsion of magnetic fields at given points on the black hole horizon. We perform a length scale analysis which indicates the emergence of two distinct length scales characterizing the magnetic field variation and strength of the Beltrami term, respectively.