Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
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...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-08-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.064 |
| _version_ | 1828343415409999872 |
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| author | Nicolas Franco |
| author_facet | Nicolas Franco |
| author_sort | Nicolas Franco |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T23:42:49Z |
| format | Article |
| id | doaj.art-ac90bed38b7f4a48bba931c47483dbb9 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-13T23:42:49Z |
| publishDate | 2010-08-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-ac90bed38b7f4a48bba931c47483dbb92022-12-22T02:24:27ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-08-016064Global Eikonal Condition for Lorentzian Distance Function in Noncommutative GeometryNicolas FrancoConnes' 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.http://dx.doi.org/10.3842/SIGMA.2010.064noncommutative geometryLorentzian distanceeikonal inequality |
| spellingShingle | Nicolas Franco Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry Symmetry, Integrability and Geometry: Methods and Applications noncommutative geometry Lorentzian distance eikonal inequality |
| title | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_full | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_fullStr | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_full_unstemmed | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_short | Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry |
| title_sort | global eikonal condition for lorentzian distance function in noncommutative geometry |
| topic | noncommutative geometry Lorentzian distance eikonal inequality |
| url | http://dx.doi.org/10.3842/SIGMA.2010.064 |
| work_keys_str_mv | AT nicolasfranco globaleikonalconditionforlorentziandistancefunctioninnoncommutativegeometry |