Extend the Killing initial data characterization beyond analytic asymptotic data

Establish the converse Killing initial data theorem for smooth, non-analytic asymptotic data in higher dimensions: namely, prove that a conformal Killing vector field satisfying the Killing initial data equation extends uniquely to a bulk Killing vector for the associated positive-cosmological-constant vacuum spacetime.

Background

The paper uses a higher-dimensional Killing initial data theorem whose converse is established only for analytic asymptotic data. In that result, a conformal Killing vector satisfying the boundary Killing initial data equation determines a unique bulk Killing vector. Extending this implication to the smooth non-analytic category would provide a general characterization of bulk symmetries directly from asymptotic data and would remove the analyticity restriction from the framework used to study asymptotic Killing horizons.