Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-07-18
Class.Quant.Grav. 26 015005, 2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages, 4 figures
Scientific paper
10.1088/0264-9381/26/1/015005
Simplicial 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.
Gentle Adrian P.
Kheyfets Arkady
McDonald Jonathan R.
Miller Warner A.
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