An extension of the Newman–Janis algorithm

The Newman-Janis algorithm is supplemented with a null rotation and applied to the tensors of the Reissner-Nordstr\"om spacetime to generate the metric, Maxwell, Ricci and Weyl tensors for the Kerr-Newman spacetime. This procedure also provides a mechanism whereby the Carter Killing tensor arises from the geodesic angular momentum tensor of the underlying Reissner-Nordstr\"om metric. The conformal Killing tensor in the Kerr-Newman spacetime is generated in a similar fashion. The extended algorithm is also applied to the Killing vectors of the Reissner-Nordstr\"om spacetime with interesting consequences. The Schwarzschild to Kerr transformation is a special case.