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This article is cited in 13 scientific papers (total in 13 papers)
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Nicolas Franco GAMASCO, Department of Mathematics, University of Namur FUNDP,
8 Rempart de la Vierge, B-5000 Namur, Belgium
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.
Keywords:
noncommutative geometry; Lorentzian distance; eikonal inequality.
Received: March 30, 2010; in final form August 6, 2010; Published online August 17, 2010
Citation:
Nicolas Franco, “Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry”, SIGMA, 6 (2010), 064, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma521 https://www.mathnet.ru/eng/sigma/v6/p64
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