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Closeness function on coarse grained Lorentzian geometries
Phys. Rev. D 113, 024034 – Published 16 January, 2026
DOI: https://doi.org/10.1103/txbf-hvz3
Abstract
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff distance function, it has the advantage of being numerically calculable for large causal sets. It thus provides a concrete and quantitative measure of continuumlike behavior in causal set theory and can be used to define a weak convergence condition for Lorentzian geometries.
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