Abstract. 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 the 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. The discrete Bianchi identity implies an algebraic relationship between deficit angles belonging to neighbouring 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.

PACS numbers: 04.20.−q, 04.60.−m, 04.60.Nc, 04.60.Gw

Print publication: Issue 24 (21 December 2004)
Received 10 June 2004, in final form 18 October 2004
Published 29 November 2004