Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
41 (2000), S. 6944-6958
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume element, some information on the topology and metric is encoded in the partial order that the causal structure induces among those points; one can then define closeness between Lorentzian geometries by comparing the sets of probabilities they give for obtaining the same posets. If the density of points is finite, one gets a pseudo-distance, which only compares the manifolds down to a finite volume scale, as illustrated here by a fully worked out example of two two-dimensional manifolds of different topology; if the density is allowed to become infinite, a true distance can be defined on the space of all Lorentzian geometries. The introductory and concluding sections include some remarks on the motivation for this definition and its applications to quantum gravity. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1288494
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