Statistical Lorentzian geometry and the closeness of Lorentzian manifolds (Q2738231)

The author presents, for the purposes of quantum gravity, a construction of a distance between Lorentzian geometries. He starts with a uniform random distribution of points in a compact Lorentz manifold and considers the probability that \(n\) randomly chosen points exhibit a causal order. From this, a pseudo-distance \(d_n\) between Lorentzian geometries is constructed. Some modification leads to a distance \(d\). Explicit formulas are given for an example.