Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-08-14
Class.Quant.Grav. 19 (2002) 4807-4816
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Grav
Scientific paper
10.1088/0264-9381/19/19/301
In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller an smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.
Pereira J. G.
Vargas Teofilo
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