Black Hole Entropy as Causal Links

TL;DR

This paper models black hole entropy using causal set theory by counting causal links crossing the horizon, finding a proportionality to the horizon area, thus supporting the idea of horizon atoms accounting for entropy.

Contribution

It introduces a causal set-based method to relate causal links crossing the horizon to black hole entropy, applicable to both equilibrium and non-equilibrium black holes.

Findings

Number of causal links is proportional to horizon area.

Supports interpretation of links as horizon atoms.

Applicable to both equilibrium and dynamic black holes.

Abstract

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 $\Sigma$. We find that this number is proportional to the horizon's area on $\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.