Wolfram Physics Q&A

Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is “causally disconnected” from the latter region (analogous to the definition of an apparent horizon in spacetime as being the region from which light rays cannot escape to future null infinity). If the disconnection is symmetric (i.e. if region 1 and region 2 are mutually unreachable), then this is analogous to a cosmological event horizon. On the other hand, if the disconnection is asymmetric (i.e. if region 1 is reachable from region 2, but not vice versa, which occurs whenever all causal edges connecting the two regions are oriented strictly in the direction of region 1), then this is analogous to a black hole event horizon.

The analog of a gravitational singularity is a spatially localized but temporally extended structure in the causal graph with an unusually high density of causal edges. For certain classes of rules, spatially localized structures with sufficiently high causal edge density necessarily break off into locally disconnected regions of the causal graph; as such, these rules can be thought of as being consistent with Penrose’s weak cosmic censorship hypothesis.