Manifold properties from causal sets using chains

2020/07/31 by Joachim Kambor, Nomaan X
Mathematics · Physics and Astronomy · #Causal sets #Causal structure #Formalism (music) #Friedmann–Lemaître–Robertson–Walker metric #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Spacetime #gr-qc

paper · pdf · doi:10.1088/1361-6382/abc8c9

30 pages, 12 figures

openalex created_date 2020/07/16 · openalex publication_date 2020/11/09 · arxiv created 2020/11/10 · arxiv updated 2020/11/11 · openalex updated_date 2026/08/05

Abstract

Abstract We study the utility of chains defined on causal sets in estimating continuum properties like the curvature, the proper time and the spacetime dimension through a numerical analysis. In particular, we show that in d S 2 and FLRW 3 spacetimes the formalism of Roy M et al 2013 Phys. Rev. D 87 044046 with slight modifications gives the right continuum properties. We also discuss a possible test of manifoldlikeness using this formalism by considering two models of non-manifoldlike causal sets. This is a part of a broader idea of the geometrical reconstruction of continuum properties given a discrete sub structure, in this case the causal set.

Citations

• The Discrete Geometry of a Small Causal Diamond
• Scalar Curvature of a Causal Set
• Emergence of spatial structure from causal sets
• The random discrete action for two-dimensional spacetime
• A new topology for curved space–time which incorporates the causal, differential, and conformal structures
• The causal set approach to quantum gravity