An asymptotic characterisation of the Kerr spacetime

TL;DR

This paper characterizes the Kerr spacetime near future null infinity using asymptotic characteristic initial data, employing conformal compactification and Killing spinor conditions to identify Kerr uniquely.

Contribution

It provides a novel characterization of Kerr spacetime based solely on data at future null infinity and an outgoing null hypersurface, utilizing the asymptotic characteristic initial value problem.

Findings

Conditions for the existence of a Killing spinor are derived.

Kerr spacetime is characterized using data at null infinity.

The approach employs Stewart's gauge and conformal compactification.

Abstract

We provide a characterisation of the Kerr spacetime close to future null infinity using the asymptotic characteristic initial value problem in a conformally compactified spacetime. Stewart's gauge is used to set up the past-oriented characteristic initial value problem. By a theorem of M. Mars characterising the Kerr spacetime, we provide conditions for the existence of an asymptotically timelike Killing vector on the development of the initial data by demanding that the spacetime is endowed with a Killing spinor. The conditions on the characteristic initial data ensuring the existence of a Killing spinor are, in turn, analysed. Finally, we write the conditions on the initial data in terms of the free data in the characteristic initial value problem. As a result, we characterise the Kerr spacetime using only a section of future null infinity and its intersection with an outgoing null hypersurface.