The Kerr-Newman metric: A Review
Tim Adamo, E. T. Newman
TL;DR
This work reviews the Kerr–Newman metric by deriving it from the Reissner–Nordström solution via Newman’s complex transformation and a scalar extension (Keane 2014), then validates the resulting Einstein–Maxwell system with spin-coefficient equations. It surveys the metric’s geometric structure across null, Boyer–Lindquist, and Kerr–Schild coordinates, and analyzes its ring singularity, horizons, and ergosphere, including implications for energy extraction and black-hole thermodynamics. The article situates Kerr–Newman within the Kerr–Schild class and discusses higher-dimensional analogues, related solutions, and limitations of complex transformation methods. Overall, it highlights a powerful solution-generating technique that deepens understanding of charged, rotating black holes and their broader theoretical context.
Abstract
The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of this metric from the Reissner-Nordstrom solution by means of a complex transformation algorithm and provide a brief overview of its basic geometric properties. We also include some discussion of interpretive issues, related metrics, and higher-dimensional analogues.