An extension of the Newman-Janis algorithm

TL;DR

This paper extends the Newman-Janis algorithm by incorporating a null rotation to derive the Kerr-Newman spacetime tensors from Reissner-Nordström, revealing new insights into Killing tensors and spacetime transformations.

Contribution

The paper introduces an extended Newman-Janis algorithm that includes null rotations, enabling derivation of Kerr-Newman tensors and Killing tensors from Reissner-Nordström spacetime.

Findings

Generated Kerr-Newman tensors from Reissner-Nordström spacetime.

Derived Carter and conformal Killing tensors via the extended algorithm.

Explored transformations from Schwarzschild to Kerr as a special case.

Abstract

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.