On Beltrami states near black hole event horizon
Abstract
In this article, we study Beltrami equilibria for plasmas 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 singlefluid approximation. We find that the horizon profile for the magnetic field is shown to satisfy a system of firstorder 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 depends only on the thermal properties of the plasma. Our analysis makes use of the full form for the timeindependent Ampère'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 the strength of the Beltrami term, respectively.
 Publication:

Physics of Plasmas
 Pub Date:
 July 2020
 DOI:
 10.1063/5.0010050
 arXiv:
 arXiv:2007.00687
 Bibcode:
 2020PhPl...27g2901B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 11 pages