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.
|Number of pages||11|
|Journal||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|Publication status||Published - 17 Aug 2010|
- Noncommutative Geometry; Lorentzian distance; eikonal inequality
Franco, N., 31 Aug 2011
Student thesis: Doc types › Doctor of SciencesFile