Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
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 …