Janis–Newman Algorithm: Generating Rotating and NUT Charged Black Holes

Abstract

Abstract:In this review we present the most general form of the Janis-Newman algorithm. This extension allows generating configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański-Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.

Born–Infeld inspired modifications of gravity

“…, allows to solve the field equations for M (x), and transforming that solution back to g µν using that {q ab = g ab Ω + ; q mn = g mn Ω − }, where (a, b) contains the 2 × 2 block and (m, n) the maximally symmetric sector, one obtains the final solution for g µν as 154) with the definition z ≡ r/r c , where r…”

“…To conclude, though many appealing results have been found in the context of Born-Infeld inspired modifications of gravity, there is plenty of room for further research in many different directions. 42 In this sense we point out that the applicability of the Janis-Newman method (which allows to obtain a rotating solution from a seed static metric, see Erbin for a review [154]) in the context of Born-Infeld inspired modifications of gravity is still to be understood. 43 Indeed, very recently it was found evidence on the existence of wormhole configurations above a certain mass threshold when a free static and spherically symmetric scalar field is let to gravitate under the BornInfeld dynamics [8].…”

Generating five-dimensional Myers–Perry black hole solution using quaternions

“…This algorithm presents an alternative way for deriving rotating solutions by applying a particular complex transformation to a non-rotating static metric in four dimensions. More details may be found in [5]. To use this algorithm, we consider the usual form of a static metric in coordinate (t, r, θ, φ) as follows:…”

“…This algorithm has been used to generate different rotating solutions. More explanations and detailed reviews can be found in [3][4][5][6][7][8][9][10]. In 1999, Kim was able to derive the AdS 3 rotating solution from the non-rotating one of Banados, Teitelboim, and Zanelli (BTZ) [11] by applying the Newman-Janis formulation.…”

Generating odd-dimensional rotating black holes with equal angular momenta by using the Kerr–Schild Cartesian form of metric

“…The five-dimensional Myers-Perry (MP) black hole solution was obtained using simplification of the NJ algorithm proposed by Giampieri [6,7,8,9,10]. The authors in [10] also proposed a simpler NJ algorithm to generate five-dimensional rotating black holes.…”