Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

Symmetry Integrability and Geometry-Methods and Applications

article

Nicolas Franco¹ 

[1] Department of Mathematics, University of Namur FUNDP

关键词: noncommutative geometry;    Lorentzian distance;    eikonal inequality;   

DOI  :  10.3842/SIGMA.2010.064

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown