Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

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

2010-03-29

arxiv.org/abs/1003.5651v2

SIGMA 6 (2010), 064, 11 pages

Physics

Mathematical Physics

Special Issue on Noncommutative Spaces and Field

Scientific paper

10.3842/SIGMA.2010.064

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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