Browsing by Author "Bray, Hubert"

We examine aspects of hypersurfaces inside initial data for the Einstein equations. We prove that 3-dimensional initial data with an apparent horizon boundary can be perturbed to data with a $H=0$, $k=0$ boundary while preserving the dominant energy condition. This yields a reduction of the spacetime Penrose conjecture to the case of $H=0$, $k=0$ boundaries. We also give an upper bound of the spacetime Bartnik mass of apparent horizon Bartnik data satisfying a stability condition in terms of the area.

Secondly, we define a new type of singularity, called a ``DEC-crease'', across a hypersurface for initial data, modeled on two spacelike slices of a spacetime meeting at a hyperbolic dihedral angle. We prove that a positive mass theorem holds for spin initial data sets containing such singularities, in any dimension. Our proof is based on Dirac-Witten spinors. At the singularity, a transmission-type boundary condition for spinors is defined and we show its ellipticity.