Bhattacharya, A and Mathur, A and Surya, S (2023) Null geodesics from ladder molecules. In: General Relativity and Gravitation, 55 (2).
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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.
| Item Type: | Journal Article |
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| Publication: | General Relativity and Gravitation |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Causal structure poset; Discrete geometry; Null geodesics; Quantum gravity |
| Department/Centre: | Division of Chemical Sciences > Inorganic & Physical Chemistry |
| Date Deposited: | 21 Feb 2023 05:13 |
| Last Modified: | 21 Feb 2023 05:13 |
| URI: | https://eprints.iisc.ac.in/id/eprint/80551 |
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