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arXiv · 2410.02178

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

Chen Lan·Zi-Xiao Liu·Yan-Gang Miao
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Abstract

We address a specific issue 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, $R=0$. 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" in order to emphasize Newman-Janis algorithm's potential 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 open an alternative avenue using the Newman-Janis algorithm for the construction of new axisymmetric black holes.

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Chen Lan, Zi-Xiao Liu, Yan-Gang Miao. 2025-11-30. Axisymmetric generalization of zero-scalar-curvature solutions from the Schwarzschild metric via the Newman-Janis algorithm. https://doi.org/10.1088/1674-1137%2Fae1184

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