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A geometric invariant measuring the deviation from Kerr data

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If you have a question about this talk, please contact David Kubiznak.

I will discuss the construction of a geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations. This invariant vanishes if and only if the data corresponds to a slice of the Kerr black hole spacetime, thus, it provides a measure of the non-Kerrness of generic data. In order to motivate the construction of the geometric invariant, I will discuss a characterisation of the Kerr spacetime using valence 2 Killing spinors this will lead to the notion of approximate Killing spinors. An approximate Killing spinor is a valence 2 symmetric spinor satisfying a system of second order linear elliptic equations. The existence of solutions to this elliptic system with the appropriate behaviour at infinity will be discussed. This is work in collaboration with T. Backdahl.

This talk is part of the DAMTP Friday GR Seminar series.

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