Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 6 |
| Issue number | 064 |
| DOIs | |
| Publication status | Published - 17 Aug 2010 |
Keywords
- Noncommutative Geometry; Lorentzian distance; eikonal inequality
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Dive into the research topics of 'Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry'. Together they form a unique fingerprint.Student theses
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Lorentzian approach to noncommutative geometry
Author: Franco, N., 31 Aug 2011Supervisor: Lambert, D. (Supervisor), Lemaitre, A. (Supervisor), Fuzfa, A. (Jury), Carletti, T. (President), MARTINETTI, P. (External person) (Jury) & LACHIEZE-REY, M. (External person) (Jury)
Student thesis: Doc types › Doctor of Sciences
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