Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry - Franco, N. (Symmetry, Integrability and Geometry: Methods and Applications, 2010)
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.