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arXiv · 1003.5651

Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Nicolas Franco
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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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Nicolas Franco. 2010-08-17. Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry. https://doi.org/10.3842/sigma.2010.064

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