The conformal Killing spinor initial data equations

We obtain necessary and sufficient conditions for an initial data set the vacuum conformal Einstein field equations to give rise a spacetime development in possession of Killing spinor. The fact that are used our derivation allows possibility hypersurface S intersecting non-trivially with (or even being subset of) null infinity I. For conciseness, these derived assuming is spacelike. Hence, particular, spinor encode existence asymptotic on spacelike components