Kerr-Schild approach to the boosted Kerr solution

Using a complex representation of the Debney-Kerr-Schild solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for an arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrarelativistic case we obtain lightlike solutions possessing diverging and twisting principal null congruences and having, contrary to the known $\mathrm{pp}$-wave limiting solutions, a nonzero value of the total angular momentum. The implications of the above results in various related fields are discussed.