Inference of boundaries in causal sets

William J Cunningham
Classical and Quantum Gravity
35 094002
April 4, 2018

Abstract

We investigate the  extrinsic geometry of causal sets in (1+1)-dimensional Minkowski spacetime.  The properties of boundaries in an embedding space can be used not only to  measure observables, but also to supplement the discrete action in the  partition function via discretized Gibbons-Hawking-York boundary terms. We  define several ways to represent a causal set using overlapping subsets,  which then allows us to distinguish between null and non-null bounding  hypersurfaces in an embedding space. We discuss algorithms to differentiate  between different types of regions, consider when these distinctions are  possible, and then apply the algorithms to several spacetime regions.  Numerical results indicate the volumes of timelike boundaries can be measured  to within 0.5% accuracy for flat boundaries and within 10% accuracy for  highly curved boundaries for medium-sized causal sets with N=214 spacetime  elements.

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