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.

4 pages, added lemma, changed references

References in corpus (3)

• An intrinsic characterization of the Kerr metric
• Killing spinor initial data sets
• On the invariant symmetries of the $\mathcal{D}$-metrics

Cited by in corpus (17)

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• The "non-Kerrness" of domains of outer communication of black holes and exteriors of stars
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• 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