2023/04/05 by Jonathan Glöckle, Glöckle, Jonathan
#math.DG #gr-qc
paper · pdf · doi:10.48550/arxiv.2304.02331
In this paper we prove an initial data rigidity result à la Eichmair, Galloway and Mendes (arXiv:2009.09527) using Dirac operator techniques. It applies to initial data sets on spin bands that satisfy the dominant energy condition, a boundary condition for the future null expansion scalar and the A-obstruction for positive scalar curvature on one of the boundary pieces. Interestingly, these bands turn out to carry lightlike imaginary W-Killing spinors, which are connected to Lorentzian special holonomy and moduli spaces of Ricci-flat metrics. We also obtain slight generalizations of known rigidity results on Riemannian bands.