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.
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页数：11
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