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Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry (1003.5651v2)
Published 29 Mar 2010 in math-ph, gr-qc, and math.MP
Abstract: 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.
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