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Title: Discrete geometry of a small causal diamond
Authors: Roy, Mriganko
Sinha, Debdeep
Surya, Sumati
Issue Date: Feb-2013
Publisher: American Physical Society
Citation: Physical Review D, 2013, Vol.87, p 044046
Abstract: We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance hCki of k-element chains or total orders in the underlying causal set C. We begin by obtaining the first-order curvature corrections to the flat spacetime expression for hCki using Riemann normal coordinates. For fixed spacetime dimension this allows us to find a new expression for the discrete scalar curvature of C as well as the time-time component of its Ricci tensor in terms of the hCki. We also find a new dimension estimator for C which replaces the flat spacetime Myrheim-Meyer estimator in generic curved spacetimes.
Description: Open Access.
ISSN: 1550-7998
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Copyright: 2013 American Physical Society
Appears in Collections:Research Papers (TP)

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