Killing spinor initial data sets

TL;DR

This paper develops conditions on initial data for Einstein's equations that ensure the development contains solutions to twistor and Killing spinor equations, aiding in classifying spacetime types.

Contribution

It introduces a 3+1 decomposition using space spinor formalism and defines twistor and Killing spinor initial data for Einstein vacuum solutions.

Findings

Characterization of initial data leading to Petrov type N or D spacetimes

Conditions for developments containing twistor or Killing spinor solutions

Framework for analyzing initial data via spinor formalism

Abstract

A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to the twistor and/or Killing equations. These lead to the notions of twistor and Killing spinor initial data. These notions are used to obtain a characterisation of initial data sets whose development are of Petrov type N or D.