Cartesian Kerr-Schild variation on the Newman-Janis ansatz

Abstract

The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman--Janis trick that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman-Janis procedure can, (using the interplay between oblate spheroidal and Cartesian coordinates), be reduced to a considerably cleaner 2-step process.

V1: 10 pages; V2; 10 pages (reformatted); 7 more references; some additional discussion; legal name change for first author

References in corpus (4)

• Sgr A* and General Relativity
• Generating exact solutions to Einstein's equation using linearized approximations
• An extension of the Newman-Janis algorithm
• The not-so-nonlinear nonlinearity of Einstein's equation

Cited by in corpus (13)

• A novel family of rotating black hole mimickers
• Charged black-bounce spacetimes
• Janis-Newman algorithm: generating rotating and NUT charged black holes
• Quasinormal modes-shadow correspondence for rotating regular black holes
• Feynman's i-epsilon prescription, almost real spacetimes, and acceptable complex spacetimes
• Unit-lapse versions of the Kerr spacetime
• Darboux diagonalization of the spatial 3-metric in Kerr spacetime
• Physically motivated ansatz for the Kerr spacetime
• Near-horizon geodesics for astrophysical and idealised black holes: Coordinate velocity and coordinate acceleration
• Complex conformal transformations and zero-rest-mass fields
• On the discrete version of the Kerr-Newman solution
• On the discrete version of the Kerr geometry
• Newman-Janis Algorithm from Taub-NUT Instantons