منابع مشابه
The Geometry of Small Causal Diamonds
The geometry of causal diamonds or Alexandrov open sets whose initial and final events p and q respectively have a proper-time separation τ small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in τ whose coefficients involve the curvature at the centre of the diamond. We give formulae for the total 4-volume V of the diamond, the are...
متن کاملThe Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes
In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set I(p) ∩ I−(q) whose duration τ (p, q) is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point q recedes to the future boundary I of an asymptotically de-Sitter spacetime. The volume (at fixed τ ) remains finite in this limit and is given b...
متن کاملThe volume of causal diamonds, asymptotically de Sitter space-times and irreversibility
In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a ma...
متن کاملGeometry of faithfulness assumption in causal inference
Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and stron...
متن کاملCausal Geometry of Rough Einstein Cmcsh Spacetime
This is the second paper of the series of two papers in which we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in Hs, s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implem...
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ژورنال
عنوان ژورنال: Physics Letters B
سال: 2007
ISSN: 0370-2693
DOI: 10.1016/j.physletb.2007.03.068