A spacetime positive mass theorem with corners via mollification

Abstract

We prove a strict dominant energy deformation theorem for asymptotically flat initial data with corners along a hypersurface $\hat{I}\pounds$. The deformation preserves a corner condition on the Bartnik data across $\hat{I}\pounds$. We show that if the dominant energy condition holds on each side of $\hat{I}\pounds$ and the Bartnik data satisfy this corner condition, then the exterior end satisfies $E\ge |P|$ in every dimension $n\ge 3$.