Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Abstract
Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a pathindependent 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 pathindependent Lorentzian distance function.
 Publication:

SIGMA
 Pub Date:
 August 2010
 DOI:
 10.3842/SIGMA.2010.064
 arXiv:
 arXiv:1003.5651
 Bibcode:
 2010SIGMA...6..064F
 Keywords:

 noncommutative geometry;
 Lorentzian distance;
 eikonal inequality;
 Mathematical Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 Special Issue on Noncommutative Spaces and Field