Discrete Geodesics and Cellular Automata

  • Pablo Arrighi
  • Gilles Dowek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9477)


This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The proposed notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation—as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length.


Discrete connection Parallel transport General relativity Regge calculus 



This work has been funded by the ANR-12-BS02-007-01 TARMAC grant, the ANR-10-JCJC-0208 CausaQ grant, and the John Templeton Foundation, grant ID 15619. Pablo Arrighi benefited from a visitor status at the IXXI institute of Lyon.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LIFAix-Marseille UniversityMarseille Cedex 9France
  2. 2.Inria, CS 81321Paris Cedex 13France

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