相关论文: On the Causal Set-Continuum Correspondence
This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…
Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of a Lorentzian lattice, or "causal set", from which continuum spacetime emerges in a large-scale…
We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open, and may differ from the…
Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations,…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
Suppose one has a party of $m$ people, whose expertise collectively covers $n$ topics. Given a subset $T$ of the topics, one wishes to form a panel of $|T|$ people from the party such that $T$ can be covered by assigning a distinct topic to…
We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of $n$ points from $[0,1]^d$ and cover-free families from the extremal set theory. This connection was discovered in a recent paper of…
Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…
Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.
A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. In this note we give…
Let $\left(a_{n}\right)_{n=1}^{\infty}$ be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all $\alpha\in\mathbb{R}$, the pair correlation of $\left(\alpha a_{n}\right)_{n=1}^{\infty}$ mod 1 is…
We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…
We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…
This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly causal Lorentzian manifolds to the corresponding category of…
The goal of the paper is to introduce a convergence \`a la Gromov-Hausdorff for Lorentzian spaces, building on $\epsilon$-nets consisting of causal diamonds and relying only on the time separation function. This yields a geometric notion of…
We report first-order spatial and temporal correlations in strongly coupled plasmonic Bose-Einstein condensates. The condensate is large, more than twenty times the spatial coherence length of the polaritons in the uncondensed system and…
We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics transverse to the foliation. In order to develop the necessary…
We show that along a density one subsequence of admissible radii, the nearest neighbor spacing between lattice points on circles is Poissonian.
In this work we revisit the notion of the (future) causal completion of a globally hyperbolic spacetime and endow it with the structure of a Lorentzian pre-length space. We further carry out this construction for a certain class of…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…