Rigidity of marginally outer trapped (hyper)surfaces with negative 𝜎-constant

Abstract

In this paper we generalize a result of Galloway and Mendes in two different situations: in the first case for marginally outer trapped surfaces (MOTSs) of genus greater than 1 1 and, in the second case, for MOTSs of high dimension with negative σ \sigma -constant. In both cases we obtain a splitting result for the ambient manifold when it contains a stable closed MOTS which saturates a lower bound for the area (in dimension 2 2 ) or for the volume (in dimension ≥ 3 \ge 3 ). These results are extensions of theorems of Nunes and Moraru to general (non-time-symmetric) initial data sets.