Duality rotations and type D solutions of Einstein-Born-Infeld theory

Within the non-linear electrodynamics of Born-Infeld type, constrained by the condition that admits the freedom of the duality rotations the explicit type D solutions, which generalize the charged Taub-NUT metric with cosmological constant, are constructed. The obtained type D solution exhausts all solutions within the considered class, assumed that the real eigenvectors of the electromagnetic field are aligned along the geodesic and shear-free principa null directions.