parameters $\lambda$ and $c$ yields an axially but not spherically symmetric, static solution of the Einstein-Vlasov system. The deviation from spherical symmetry is small but by a scaling argument the solution can be made fully relativistic, i.e. $c=1$. In [@akr14] further technical insights made it possible to include rotation into the picture.

Lichtenstein developed a method based on the implicit function theorem to construct rotating fluid bodies [@l18; @l33] in Newtonian gravity. This approach has later been reformulated in a modern mathematical language [@h94] and improved [@h95]. In [@abs08; @abs09] the authors use an implicit function argument to construct axially symmetric static and rotating elastic bodies in Einstein gravity. In a series of papers of which the last one is [@cdkkmr18] the authors construct stationary solutions of the Einstein equations with negative cosmological constant without any symmetries. Many different matter models can be included, such as a scalar field, Maxwell, or Yang-Mills.

Space-times with rotating, charged matter configurations have been studied in the literature by analytical and numerical means, see e.g. [@bbgn95; @cpl00; @fr12]. An important motivation for these studies is the modelling of rotating stars or neutron stars with a magnetic field. In these articles the matter is modelled 