Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry

被引：15

作者：

Franco, Nicolas ^{[1
]}

机构：

[1] Univ Namur FUNDP, GAMASCO, Dept Math, B-5000 Namur, Belgium

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2010年 / 6卷

关键词：

noncommutative geometry; Lorentzian distance; eikonal inequality; HYPERBOLIC SPACETIMES; VARIABLES;

D O I：

10.3842/SIGMA.2010.064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：11

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