takes into account gravity, particles described by the EVM-system are not freely falling, i.e. their trajectories are not geodesics.

In this article the existence of stationary, rotating solutions of the EVM-system is proven by means of the implicit function theorem. The proof is a generalisation of [@akr14], where the existence of rotating, stationary solutions of the Einstein-Vlasov system with uncharged particles is proved, to the case where the particles are charged and hence induce an electro-magnetic field. In the context of kinetic theory this method has already been used in [@r00] to show the existence of stationary, rotating solutions of the Vlasov-Poisson system. The idea of this method is to introduce a parameter $\lambda$ to the system which can “turn on” rotation and to perturb the system around a spherically symmetric, static solution without rotation. To this end one considers a functional $\mathfrak F : \mathcal X \times [-\delta,\delta]\to \mathcal X$, where $\mathcal X$ is a suitable function space which will contain the solution and $[-\delta, \delta]$ is the interval in which the parameter $\lambda$ will lie. The operator is constructed such that if $\mathfrak F(\zeta,\lambda) = 0$ then $\zeta$ is a collection of functions which constitute a solution of 