Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity

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dc.creatorRaptis, Ioannis
dc.date2005-07-24
dc.date2005-09-21
dc.date.accessioned2026-07-07T10:28:11Z
dc.date.available2026-07-07T10:28:11Z
dc.descriptionPrevious work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure. This topos is seen to be a finitary instance of both an elementary and a Grothendieck topos, generalizing in a differential geometric setting, as befits ADG, Sorkin's finitary substitutes of continuous spacetime topologies. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research.
dc.description49 pages, latest updated version (errata corrected, references polished) Submitted to the International Journal of Theoretical Physics
dc.identifierhttps://arxiv.org/abs/gr-qc/0507100
dc.identifierhttp://arxiv.org/abs/gr-qc/0507100
dc.identifierInt.J.Theor.Phys.46:688-739,2007
dc.identifierdoi:10.1007/s10773-006-9240-y
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/177361
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleFinitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
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