Stationary Einstein-Maxwell fields in arbitrary dimensions

The Einstein-Maxwell equations in D dimensions admitting $\left(D-3\right)$ commuting Killing vector fields have been investigated. The existence of the electric, magnetic, and twist potentials has been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electromagnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and the static charged black ring solution.