Axisymmetric generalization of zero-scalar-curvature solutions from the Schwarzschild metric via the Newman-Janis algorithm*

Abstract We address a specific problem of the Newman-Janis algorithm: how to determine the general form of the complex transformation for the Schwarzschild metric and ensure that the resulting axisymmetric metric satisfies the zero-scalar-curvature condition . In this context, the zero-scalar-curvature condition acts as a constraint. Owing to this condition, we refer to the class of black holes as the "Newman-Janis class of Schwarzschild black holes" to emphasize the potential of the Newman-Janis algorithm as a classification tool for axisymmetric black holes. The general complex transformation we derive not only generates the Kerr, Taub-NUT, and Kerr-Taub-NUT black holes under specific choices of parameters but also suggests the existence of additional axisymmetric black holes. Our findings create an alternative avenue using the Newman-Janis algorithm to construct new axisymmetric black holes.