Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

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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.
Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume6
Issue number064
DOIs
Publication statusPublished - 17 Aug 2010

Keywords

  • Noncommutative Geometry; Lorentzian distance; eikonal inequality

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