Abstract
Marginally outer trapped surfaces (MOTS) are special types of codimension-two space-like surfaces in Lorentzian space-times defined by the vanishing of one of its future null expansions. Such surfaces play an important role in gravitational theory as indicators of strong gravitational fields and share some of the properties of minimal hypersurfaces, in particular the existence of a useful notion of stability. In this contribution I describe this notion and present some of its consequences. In particular I will summarize the implications of stability on the topology of MOTS, their role as barriers, the interplay between stability and space–times symmetries and the stability of Killing horizons.
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