Janis-Newman algorithm: simplifications and gauge field transformation

TL;DR

This paper generalizes the Janis-Newman algorithm to include gauge field transformations, simplifies the procedure, and demonstrates its application on the Kerr-Newman solution, enhancing the method's consistency and utility.

Contribution

It introduces a systematic way to transform gauge fields within the Janis-Newman algorithm and simplifies the existing procedure.

Findings

Successfully extended the algorithm to gauge fields.

Simplified the transformation process.

Applied the method to Kerr-Newman solution.

Abstract

The Janis-Newman algorithm is an old but very powerful tool to generate rotating solutions from static ones through a set of complex coordinate transformations. Several solutions have been derived in this way, including solutions with gauge fields. However, the transformation of the latter was so far always postulated as an ad hoc result. In this paper we propose a generalization of the procedure, extending it to the transformation of the gauge field. We also present a simplification of the algorithm due to G. Giampieri. We illustrate our prescription on the Kerr-Newman solution.