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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/7198
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dc.contributor.authorEichhorn, Astrid-
dc.contributor.authorSurya, Sumati-
dc.contributor.authorVersteegen, Fleur-
dc.date.accessioned2019-05-03T18:24:34Z-
dc.date.available2019-05-03T18:24:34Z-
dc.date.issued2019-04-15-
dc.identifier.citationClassical and Quantum Gravity, 2019, Vol. 36, p105005 (35pp)en_US
dc.identifier.issn1361-6382-
dc.identifier.urihttp://hdl.handle.net/2289/7198-
dc.descriptionRestricted Accessen_US
dc.description.abstractMotivated by the Hawking–King–McCarthy–Malament (HKMM) theorem and the associated reconstruction of spacetime geometry from its causal structure and local volume element , we define a one-parameter family of spatial distance functions on a Cauchy hypersurface using only and . The parameter corresponds to a 'mesoscale' cut-off which, when appropriately chosen, provides a distance function which approximates the induced spatial distance function to leading order. This admits a straightforward generalisation to the discrete analogue of a Cauchy hypersurface in a causal set. For causal sets which are approximated by continuum spacetimes, this distance function approaches the continuum induced distance when the mesoscale is much smaller than the scale of the extrinsic curvature of the hypersurface, but much larger than the discreteness scale. We verify these expectations by performing extensive numerical simulations of causal sets which are approximated by simple spacetime regions in 2 and 3 spacetime dimensions.en_US
dc.language.isoenen_US
dc.publisherIOP Publishing Ltd.en_US
dc.relation.urihttps://arxiv.org/abs/1809.06192v1en_US
dc.relation.urihttps://doi.org/10.1088/1361-6382/ab114ben_US
dc.relation.urihttps://ui.adsabs.harvard.edu/abs/2018arXiv180906192E/abstracten_US
dc.rights2019 IOP Publishing Ltden_US
dc.subjectcausal structureen_US
dc.subjectquantum gravityen_US
dc.subjectcausal setsen_US
dc.titleInduced spatial geometry from causal structureen_US
dc.typeArticleen_US
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