Duality rotations and type D solutions to Einstein equations with nonlinear electromagnetic sources

Within nonlinear electrodynamics of Born–Infeld type allowing for the freedom of duality rotations, explicit type D solutions are constructed. The obtained type D solutions, which generalize the charged Taub–NUT (Newman–Unti–Tamburino) metric with λ, exhaust all solutions within the considered class, under the assumption that the real eigenvectors of the electromagnetic field are aligned along the geodesic and shear-free principal null directions. Various relevant limiting transitions, in particular those of the flat space-time, are studied in some detail.