Black Holes and Trapped Surfaces

Abstract

The relation between the presence of closed trapped surfaces and the existence of black holes is reviewed paying special attention to the possibility of defining the surface of the latter. Closed future‐trapped surfaces are believed to signal the formation of black holes and its event horizon. Trapped surfaces are, however, easier to handle, as they can be defined locally—contrary to event horizons, which must be defined globally. This is especially important in numerical relativity, and has led to the quasi‐local definitions of dynamical and trapping horizons. Nevertheless, it has become clear recently that closed trapped surfaces may extend outside any dynamical horizon associated to a black hole in evolution. Actually, closed trapped surfaces can even intersect flat portions of spacetime. These surprising results open new questions concerning the definition and characterization of dynamical black holes, and of what can be considered their external surface.