# Rotating Clouds of Charged Vlasov Matter in General Relativity

## TL;DR

This paper proves the existence of stationary, axially symmetric solutions to the Einstein-Vlasov-Maxwell system, including rotating configurations with electric and magnetic fields, extending previous uncharged particle results.

## Contribution

It generalizes prior methods to include charged particles, demonstrating the existence of rotating solutions with specific electromagnetic field configurations.

## Key findings

- Existence of stationary solutions with axial symmetry.
- Rotating solutions induce poloidal magnetic fields.
- Toroidal magnetic field components are not possible.

## Abstract

The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of an article by H{\aa}kan Andr\'easson, Markus Kunze and Gerhard Rein where a similar result is obtained for uncharged particles. Among the solutions constructed in this article there are rotating and non-rotating ones. Static solutions exhibit an electric but no magnetic field. In the case of rotating solutions, in addition to the electric field, a purely poloidal magnetic field is induced by the particle current. The existence of toroidal components of the magnetic field turns out to be not possible in this setting.