Discrete Gravity as a Local Theory of the Poincaré Group in the First Order Formalism

Details Discrete Gravity as a Local Theory of the Poincaré Group in the First Order Formalism Discrete Gravity as a Local Theory of the Poincaré Group in the First Order Formalism

2005-01-26

arxiv.org/abs/gr-qc/0501082v2

Class.Quant.Grav. 22 (2005) 4217-4230

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version, 18 pages, 2 figures, accepted by Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/22/20/004

A discrete theory of gravity locally invariant under the Poincar\'e group is considered as in a companion paper. We define a first order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit of the continuum theory of General Relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first order Einstein equations in the Cartan formalism. It is shown that in the limit of {\it small deficit angles} these equations have Regge Calculus, locally, as the only solution. A quantum measure is easly defined which does not suffer the ambiguities of Regge Calculus, and a coupling with fermionic matter is easily introduced

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