Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Discrete Geometry of a Small Causal Diamond   We study the discrete causal set geometry of a small causal diamond in a
curved spacetime using the average abundance 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 the abundance 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 abundances of k-chains.
We also find a new dimension estimator for C which replaces the flat spacetime
Myrheim-Meyer estimator in generic curved spacetimes.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph