On the Bianchi identity in generalized theories of gravity

Abstract

We examine the generalised Bianchi identity, ∇a Eab = 0 where Eab is the equation of motion tensor of a general class of theories of gravity whose Lagrangian L(gab, Ra bcd ) depends arbitrarily on gab and Ra bcd but not on the covariant derivative of Ra bcd . We derive interesting identities related to the divergence of Eab which are intimately related to the diffeomorphism invariance property of such theories of gravity. The implications are discussed.