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.
