Black Hole Entropy as Causal Links

We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface $\mathrm{\Sigma }$. We find that this number is proportional to the horizon’s area on $\mathrm{\Sigma }$, thus supporting the interpretation of the links as the ``horizon atoms’’ that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.