Gyromagnetic factor of rotating disks of electrically charged dust in general relativity

TL;DR

This paper computes the gyromagnetic ratio of rotating, charged dust disks in general relativity, revealing how it varies with relativistic effects and charge, bridging Newtonian and black-hole limits.

Contribution

It provides a detailed analysis of the gyromagnetic ratio for charged dust disks, connecting Newtonian and relativistic regimes within Einstein-Maxwell solutions.

Findings

g approaches 1 in the Newtonian limit

g approaches 2 in the black-hole limit

g varies smoothly with relativistic parameter b3 and charge b5

Abstract

We calculated the dimensionless gyromagnetic ratio ("$g$-factor") of self-gravitating, uniformly rotating disks of dust with a constant specific charge $\epsilon$. These disk solutions to the Einstein-Maxwell equations depend on $\epsilon$ and a "relativity parameter" $\gamma$ ($0<\gamma\le 1$) up to a scaling parameter. Accordingly, the $g$-factor is a function $g=g(\gamma,\epsilon)$. The Newtonian limit is characterized by $\gamma \ll 1$, whereas $\gamma\to 1$ leads to a black-hole limit. The $g$-factor, for all $\epsilon$, approaches the values $g=1$ as $\gamma\to 0$ and $g=2$ as $\gamma\to 1$.