Title:	Null geodesics from ladder molecules
Authors:	Bhattacharya, Anish Abhishek, Mathur Surya, Sumati
Keywords:	discrete geometry quantum gravity causal structure poset null geodesics
Issue Date:	4-Feb-2023
Publisher:	Springer
Citation:	General Relativity and Gravitation, 2023, Vol. 55, Article No.32
Abstract:	We propose a discrete analogue of null geodesics in causal sets that are approximated by M2, in the spirit of Kronheimer and Penrose’s ”grids” and ”beams” for an abstract causal space. The causal set analogues are “ladder molecules”, whose rungs are linked pairs of elements corresponding loosely to Barton et al’s horizon bi-atoms [1]. In M2 a ladder molecule traps a ribbon of null geodesics corresponding to a thickened or fuzzed out horizon. The existence of a ladder between linked pairs of elements in turn provides a generalisation of the horismotic relation to causal sets. Simulations of causal sets approximated by a region of M2 show that ladder molecules are fairly dense in the causal set, and provide a light-cone like grid. Moreover, similar to the uniqueness of null geodesics between horismotically related events in M2, in such causal sets there is a unique ladder molecule between any two linked pairs which are related by the generalised horismotic relation.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/8063
ISSN:	0001-7701 1572-9532 (Online)
Alternative Location:	https://arxiv.org/abs/2301.06480 https://ui.adsabs.harvard.edu/abs/2023GReGr..55...32B/abstract https://inspirehep.net/literature/2623883 https://doi.org/10.1007/s10714-023-03074-y
Copyright:	2023 The Author(s)
Appears in Collections:	Research Papers (TP)

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