Talk abstract details

We prove that in asymptotically untrapped static spacetimes satisfying the dominant energy condition (DEC), any marginally outer trapped surface (MOTS) cannot penetrate the exterior region where the static Killing vector is timelike. In fact we prove this result at the initial data level, without even assuming existence of the spacetime. The proof relies on a powerful theorem by Schoen and Andersson \& Metzger on existence of outermost marginally outer trapped surfaces. As an application we prove uniqueness of asymptotically flat static initial data containing a MOTS provided DEC. This uniqueness result generalizes a theorem by P. Miao in the case of time symmetric initial data and vacuum.