A Space-Time Characterization of the Kerr–Newman Metric

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.

A Geometric Invariant Characterising Initial Data for the Kerr–Newman Spacetime

“…In [14], the following result has been proved: The above result is a consequence of the characterisation of the KerrNewman spacetime given in [24]. It replaces the assumption on the self-dual Weyl tensor of the spacetime with the (stronger) assumption of the existence of a Killing spinor.…”

Killing spinors as a characterisation of rotating black hole spacetimes

“…In the remainder of this article we will be particularly interested in spacetimes with a stationary asymptotically flat 4-end -see e.g. [22].…”

“…The characterisation of the Kerr spacetime by Mars given in [16] relies on a previous characterisation of this solution to the vacuum Einstein field equations in terms of the vanishing of the so-called Mars-Simon tensor -see [15]. Interestingly, the latter characterisation has been generalised to the electrovacuum case by Wong [22] assuming some restrictions on the matter content. This characterisation is not optimal -in the sense that it assumes the existence of certain relations among the relevant geometric objects; by contrast, in [15], the existence of the vacuum counterpart of these relations is a consequence of the characterisation.…”

“…This characterisation is not optimal -in the sense that it assumes the existence of certain relations among the relevant geometric objects; by contrast, in [15], the existence of the vacuum counterpart of these relations is a consequence of the characterisation. Nevertheless, as a consequence of the analysis in [22], one may expect that the Kerr-Newman solution can be characterised by the use of Killing spinors in a similar way to the vacuum case. The characterisations in both [15] and [22] come in both a local version (in which certain constraints arising in the characterisation are fixed by evaluating them at finite points of the manifold) and a global version (in which asymptotic flatness is used to fix the value of the constants).…”

Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

“…Later, Mars [112], see also Mars [111] and Mars & Senovilla [113], generalized this approach and was led to the 4d "Simon-Mars tensor". In Ionescu & Klainerman [88], one can find a more extended discussion of the Simon-Mars tensor, see also Wong [192]. More recently, Bäckdahl & Valiente Kroon [9] have proposed replacing the Simon-Mars tensor by another measure of "non-Kerrness", namely a scalar parameter.…”