Manifold dimension of a causal set: Tests in conformally flat spacetimes

TL;DR

This paper introduces a method to estimate the manifold dimension of causal sets embedded in curved spacetimes using flat-spacetime estimators, demonstrating its invariance and applicability across various conformally flat spacetimes.

Contribution

It presents a novel, invariant approach for estimating manifold dimensions of causal sets in curved spacetimes, independent of specific geometries.

Findings

Effective dimension estimation in conformally flat spacetimes

Applicability across 2, 3, and 4 dimensions

Compatibility with causal sets generated by different methods

Abstract

This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can be implemented independently of any specific curved spacetime. Results are given based on causal sets generated by random sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well as one generated by a percolation dynamics.