The conformal Killing spinor initial data equations

TL;DR

This paper derives necessary and sufficient conditions for initial data in vacuum conformal Einstein equations to produce spacetimes with Killing spinors, including cases where the initial surface intersects null infinity, aiding understanding of spacetime symmetries.

Contribution

It provides the first complete characterization of initial data conditions for the existence of Killing spinors in conformal Einstein spacetimes, including at null infinity.

Findings

Conditions are derived for initial data to admit a Killing spinor.

The results apply even when the initial hypersurface intersects null infinity.

These conditions are both necessary and sufficient.

Abstract

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