A space-time characterization of the Kerr-Newman metric

TL;DR

This paper extends the characterization of the Kerr metric to the Kerr-Newman family by analyzing the alignment of electromagnetic and curvature fields, providing new geometric criteria for identifying these spacetimes.

Contribution

It introduces a novel characterization of Kerr-Newman spacetimes based on simultaneous alignment conditions involving Maxwell, Ernst, and Weyl fields.

Findings

Alignment conditions imply local isometry to Kerr-Newman

Extension of null tetrad formalism to include Ricci curvature

Generalization of Mars's Kerr characterization

Abstract

In the present paper, the characterization of the Kerr metric found by Marc Mars is extended to the Kerr-Newman family. A simultaneous alignment of the Maxwell field, the Ernst two-form of the pseudo-stationary Killing vector field, and the Weyl curvature of the metric is shown to imply that the space-time is locally isometric to domains in the Kerr-Newman metric. The paper also presents an extension of Ionescu and Klainerman's null tetrad formalism to explicitly include Ricci curvature terms.