From conformal to Einstein Gravity

Abstract

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.

Improved discussion on Einstein spaces in CG. Reference list updated. Final version for PRD

References in corpus (5)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Critical Gravity in Four Dimensions
• Holographic two-point functions for 4d log-gravity
• Renormalized AdS action and Critical Gravity
• Holographic Two-Point Functions in Conformal Gravity

Cited by in corpus (3)

• Near-extremal black holes in Weyl gravity: Quasinormal modes and geodesic instability
• Black hole solutions correspondence between conformal and massive theories of gravity
• Holographic correlation functions in Critical Gravity