 For the reasons discussed in  section 3.1,  the standard definition of a black hole, based on the idea of a global event horizon, has limited application to the modeling of real astrophysical systems (except in so far as one can idealize them as essentially isolated). In an attempt to rectify this situation, Hayward (1994b) offered a generalized definition of a black hole, not requiring any of the special global structures that the traditional definition relies on. Hayward defines a black hole based on what he calls a trapping horizon. This is, roughly speaking, a surface on which all inward-directed light rays are converging, and to which all outward-directed light rays are tangent. This definition tries to capture the idea that a black hole is a surface at which the gravitational intensity is such that not even light can escape: any light ray incident on the surface the smallest bit inward will get sucked in; otherwise, light rays can be only tangent to the surface. The surface does not admit incident light rays traveling away from its interior. This definition has the virtue that the boundary of the black hole now has clear, local physical significance in principle: an observer could determine when she crossed it by making only local measurements. (More precisely, a team of synchronized observers, whose combined instrumental reach encompasses the entire surface at a given moment of time, could jointly make this determination, with enough background knowledge of the spacetime geometry outside the boundary.) Perhaps one of the most intriguing aspects of Hayward's definition is that a black hole would not necessarily be a region of no escape: in some black holes so defined, an observer entering the trapped region could later escape it (Hayward 1994a, in OIR).  