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

This paper describes an approach that uses flat-spacetime 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.