but no toroidal magnetic field.

We briefly mention that in the non-relativistic setting a variety of different axially symmetric solutions can be constructed explicitly, cf. for example [@galactic_dynamics]. A well studied class of these solutions are disk solutions which serve as models for disk shaped galaxies and which are used to study some physical properties of these galaxies. The so called Morgan & Morgan disk solutions, introduced in [@mm69], are important in this context. In [@rap12] the authors construct comparable axially symmetric solutions in Newtonian gravity with general relativistic corrections. Surprisingly these general relativistic corrections account for changes of the solutions far from the galaxy core – a region where it was expected that Newtonian gravity describes the physics well and general relativistic effects do not play a significant role. This observation adds to the motivation of studying axially symmetric configurations of collisionless particles in the fully general relativistic picture.

The present article generalises [@akr14] to the case of charged particles, i.e.  solutions of the EVM-system are constructed by perturbing off a non-trivial, spherically symmetric, static solution of the Vlasov-Poisson system. It is assumed that the particles are charged with a particle charge $q$, i.e. an electro-magnetic field is included 