Horizon Molecules in Causal Set Theory

TL;DR

This paper introduces a new way to define and analyze horizon molecules in Causal Set Theory, linking their expected count to horizon area and enabling extraction of geometric information.

Contribution

It proposes a novel definition of horizon molecules applicable to any causal horizon and intersection, with detailed analysis of their expected number and corrections in the continuum limit.

Findings

Expected number of horizon molecules scales with horizon area

First order corrections reveal additional geometric information

Method applicable to any causal horizon and spacelike hypersurface

Abstract

We propose a new definition of "horizon molecules" in Causal Set Theory following pioneering work by Dou and Sorkin. The new concept applies for any causal horizon and its intersection with any spacelike hypersurface. In the continuum limit, as the discreteness scale tends to zero, the leading behaviour of the expected number of horizon molecules is shown to be the area of the horizon in discreteness units, up to a dimension dependent factor of order one. We also determine the first order corrections to the continuum value, and show how such corrections can be exploited to obtain further geometrical information about the horizon and the spacelike hypersurface from the causal set.