In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets that contain no (immersed) marginally outer trapped surfaces in their interior must have simple topology: they are a product of a surface and an interval, or a mild variation thereof, depending on the connectedness of the horizon and on its genus relative to that of the end. The results obtained here extend results in Eichmair et al. (J Differ Geom 95:389–405, 2013) to the case of higher genus ends.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics