Time-oriented null hypersurfaces in Lorentzian manifolds are one-way barriers for causal curves, enabling definitions of barriers and black regions that generalize smooth event horizons and black holes.
Penrose,Structure of space-time, in Battelle rencontres - 1967 lectures in mathematics and physics: Seattle, WA, USA, 16 - 31 July 1967”, C.M
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Black holes and black regions, horizons and barriers in Lorentzian manifolds
Time-oriented null hypersurfaces in Lorentzian manifolds are one-way barriers for causal curves, enabling definitions of barriers and black regions that generalize smooth event horizons and black holes.