On the Bianchi identity in generalized theories of gravity

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

Automated summary

We examine the generalised Bianchi identity, del E-a(ab) = 0, in a general class of gravity theories. We derive interesting identities related to the divergence of E-ab which are intimately connected to the diffeomorphism invariance property of such theories. The implications of these results are discussed.