On the construction of a geometric invariant measuring the deviation from Kerr data

Understand

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations.

• This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data.
• The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean.
• As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out.