Exact Bianchi Identity in Regge Gravity

Details Exact Bianchi Identity in Regge Gravity Exact Bianchi Identity in Regge Gravity

2001-07-10

arxiv.org/abs/gr-qc/0107031v2

Class.Quant.Grav. 21 (2004) 5915-5948

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 45 pages, 6 figures, revised & expanded, references added

Scientific paper

10.1088/0264-9381/21/24/013

In the continuum the Bianchi identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. It implies an algebraic relationship between deficit angles belonging to neighboring hinges. As in the continuum, the derived identity is valid for arbitrarily curved manifolds, without a restriction to the weak field, small curvature limit, but is in general not linear in the curvatures.

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