title: Geometric invariant measuring the deviation from Kerr data.
abstract: A geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations is constructed. This invariant vanishes if and only if the data correspond to a slice of the Kerr black hole spacetime--thus, it provides a measure of the non-Kerr-like behavior of generic data. In order to proceed with the construction of the geometric invariant, we introduce the notion of approximate Killing spinors.
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom. t.backdahl@qmul.ac.uk
authors.forename: Thomas
authors.initials: T
authors.lastname: Bäckdahl
authors.forename: Juan A
authors.initials: JA
authors.lastname: Valiente Kroon