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The first exact rotating charged black hole solution to the Einstein-nonlinear electrodynamics theory is reported. It is equipped with mass, rotation parameter, electric and magnetic charges, and three parameters due to the electrodynamics: β is associated to the potential vectors Aµ and ⋆ Pν, and two constants, F0 and G0, related to the presence of the invariants F and G in the Lagrangian L(F, G). This Petrov type D solution is characterized by the Weyl tensor eigenvalue Ψ2, the Ricci tensor eigenvalue S = 2Φ (11) , and the scalar curvature R; it allows for event horizons, exhibits a ring singularity and fulfils the energy conditions. Its Maxwell limit is the Kerr-Newman black hole.

By means of a linear Superposition of a couple of tetrads, determining a selfdual type N @flat space and an anti-self-dual flat @ type N field, the most general non.twisting type N real vacuum solution of the Einstein equation is constructed.

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