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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 relies on the methods of [@akr14] 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.'
author:
- Maximilian Thaller
title: Rotating Clouds of Charged Vlasov Matter in General Relativity
---

Introduction
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The Einstein-Vlasov-Maxwell system (EVM-system) describes an ensemble of charged particles whose motion is governed by gravity and an electro-magnetic field but which do not interact via collisions. In the framework of General Relativity gravity is described by the curvature of the manifold, the space-time, on which the particles live. Both the space-time curvature and the electro-magnetic field are generated collectively by the particles themselves. In contrast to the Einstein-Vlasov system, which only 