منابع مشابه
Statistical Lorentzian geometry and the closeness of Lorentzian manifolds
I introduce a closeness function between causal Lorentzian geometries of finite volume and arbitrary underlying topology. The construction uses the fact that some information on the manifolds and metrics is encoded in the partial order that the causal structure of each metric induces among points randomly scattered in the corresponding manifold with uniform, finite density according to the volu...
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In Lorentzian geometry, the concept of trapped submanifold is introduced by means of the mean curvature vector properties. Trapped submanifolds are generalizations of the standard maximal hypersurfaces and minimal surfaces, of geodesics, and also of the trapped surfaces introduced by Penrose. Selected applications to gravitational theories are mentioned.
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Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated in a background-independent way. After summarizing the status quo of discrete covariant lattice mod...
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We argue that the Lorentzian path integral is a better starting point for quantum cosmology than its Euclidean counterpart. In particular, we revisit the minisuperspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Pica...
متن کاملLimit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhe...
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ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2012
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2012.v16.n4.a3