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.

arXiv comment4 pages, added lemma, changed references

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Cited by in corpus (17)

• On choosing the start time of binary black hole ringdown
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• On the construction of a geometric invariant measuring the deviation from Kerr data
• Spinors: a Mathematica package for doing spinor calculus in General Relativity
• The "non-Kerrness" of domains of outer communication of black holes and exteriors of stars
• Spin geometry and conservation laws in the Kerr spacetime
• Constructing "non-Kerrness" on compact domains
• A local non-negative initial data scalar characterisation of the Kerr solution
• Approximate twistors and positive mass
• A set of invariant quality factors measuring the deviation from the Kerr metric
• A formalism for the calculus of variations with spinors
• Conformal Killing Initial Data
• Killing spinors as a characterisation of rotating black hole spacetimes
• Dain's invariant on non-time symmetric initial data sets
• Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. I. A space-time approach
• A geometric invariant characterising initial data for the Kerr-Newman spacetime
• Perturbations of Kerr with approximate Killing spinors -- Wave version