A Kirchhoff-like conservation law in Regge calculus

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dc.creatorGentle, Adrian P.
dc.creatorKheyfets, Arkady
dc.creatorMcDonald, Jonathan R.
dc.creatorMiller, Warner A.
dc.date2008-07-18
dc.date2009-03-24
dc.date.accessioned2026-07-07T12:55:08Z
dc.date.available2026-07-07T12:55:08Z
dc.descriptionSimplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einstein's geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E. Cartan moment of rotation operator. This identity manifests itself in the conceptually-simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge Calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.
dc.description13 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0807.3041
dc.identifierhttp://arxiv.org/abs/0807.3041
dc.identifierClass.Quant.Grav. 26 015005, 2009
dc.identifierdoi:10.1088/0264-9381/26/1/015005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224163
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA Kirchhoff-like conservation law in Regge calculus
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