An explanation of the Newman-Janis Algorithm

TL;DR

This paper clarifies the theoretical basis of the Newman-Janis algorithm, explaining why it successfully derives the Kerr-Newman metric and identifying the unique solutions it produces in Einstein-Maxwell theory.

Contribution

It provides a rigorous explanation for the Newman-Janis algorithm's success and characterizes the solutions it generates in Einstein-Maxwell equations.

Findings

The Newman-Janis algorithm's success is theoretically justified.

The only perfect fluid solution generated is the Kerr metric.

The Kerr-Newman metric is the unique Petrov type D solution from the algorithm.

Abstract

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.