Approximate twistors and positive mass

Details Approximate twistors and positive mass Approximate twistors and positive mass

2010-11-16

arxiv.org/abs/1011.3712v2

Class.Quant.Grav.28:075010,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, corrected typos, updated references

Scientific paper

10.1088/0264-9381/28/7/075010

In this paper the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. This is not done in a coordinate sense, but through quantification of the deviation from a specific symmetry. In a recent paper [T. B\"ackdahl, J.A. Valiente Kroon, Phys. Rev. Lett. 104, 231102 (2010)] this problem was studied with the Kerr solution as a reference solution. This analysis was based on valence 2 Killing spinors. In order to better understand this construction, in the present article we analyse the analogous construction for valence 1 spinors solving the twistor equation. This yields an invariant that measures how much the initial data deviates from Minkowski data. Furthermore, we prove that this invariant vanishes if and only of the mass vanishes. Hence, we get a proof of the positivity of mass.

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