  Connes' noncommutative Riemannian distance formula is constructed in two
steps, the first one being the construction of a path-independent geometrical
functional using a global constraint on continuous functions. This paper
generalizes this first step to Lorentzian geometry. We show that, in a globally
hyperbolic spacetime, a single global timelike eikonal condition is sufficient
to construct a path-independent Lorentzian distance function.
