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

Abstract The Newman–Janis (NJ) method is a prescription to derive the Kerr space–time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers–Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional ( d > 6 ) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the five-dimensional MP metric with two arbitrary angular momenta by using the Kerr–Schild form of the metric and quaternions. Then, we present another new two-step version of the NJ approach without using quaternions that generate the five-dimensional MP metric with equal angular momenta. Finally, the extension of the later procedure is explained for the higher odd-dimensional rotating black holes ( d > 5 ) with equal angular momenta.