M$ we have coordinates $t$, $x^1$, $x^2$, $x^3$, where $t$ is the time coordinate. Assume further that $\partial_t$ is a Killing field. Then the solution is asymptotically flat if the boundary conditions $$\label{bc_as_flat}
\lim_{|x|\to \infty} g = \eta, \quad \lim_{|x|\to \infty} f = 0, \quad \lim_{|x|\to \infty} F = 0$$ are satisfied, where $\eta$ denotes the Minkowski metric.

The result {#sect_result}
==========

In this article we prove the following result.

\[main\_theorem\] There exist asymptotically flat, stationary solutions $(g, f, F) \in (T^*\mathscr M \otimes T^*\mathscr M) \times C_c^1 (\mathscr P; \mathbb R_+) \times \Lambda^2(\mathscr M)$ of the EVM-system (\[eq\_einstein\])–(\[maxwell\_eq\_2\]) with particle charge parameters $q\in [0,1)$, which are axially symmetric but not spherically symmetric. Such a solution has no toroidal magnetic field and it has a poloidal magnetic field if and only if the solution is not static, i.e. rotating.

The proof which is given at this place is rather an outline of the poof, the technical details are given in the subsequent sections. The proof follows the same structure as in [@akr14] where the existence of stationary, rotating, axially symmetric solutions is proved for uncharged particles. Each step is however a bit more involved and some arguments have to be 