Convergence of combinatorial gravity

Christy Kelly, Fabio Biancalana, Carlo Trugenberger

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Abstract

We present a new regularization of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its manifold counterpart on sufficiently dense random geometric graphs (more generally on any sequence of graphs that converges suitably to the manifold in the sense of Gromov-Hausdorff). Our construction relies crucially on the Ollivier curvature of optimal transport theory. Our methods also allow us to define an analogous discrete action for Klein-Gordon fields. These results are part of the ongoing program combinatorial approach to quantum gravity where we seek to generate graphs that approximate manifolds as metric-measure structures.

Original languageEnglish
Article number124002
JournalPhysical Review D
Volume105
Issue number12
Early online date10 Jun 2022
DOIs
Publication statusPublished - 15 Jun 2022

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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