  We provide a simple derivation of the equivalence between Einstein and
Conformal Gravity (CG) with Neumann boundary conditions given by Maldacena. As
Einstein spacetimes are Bach flat, a generic solution to CG would contain both
Einstein and non-Einstein part. Using this decomposition of the spacetime
curvature in the Weyl tensor, makes manifest the equivalence between the two
theories, both at the level of the action and the variation of it. As a
consequence, we show that the on-shell action for Critical Gravity in four
dimensions is given uniquely in terms of the Bach tensor.

High Energy Physics - Theory;General Relativity and Quantum Cosmology