Energy functionals from Conformal Gravity

Abstract

We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal Gravity action in a manifold with a conical defect produces a codimension-2 conformal invariant functional $L_{\Sigma }$. The energy functionals are then particular cases of $L_{\Sigma }$ for Einstein-AdS and pure AdS ambient spaces, respectively. The bulk action is finite for AdS asymptotics and both Hawking mass and Willmore energy are finite as well. The result suggests a generic relation between conformal invariance and renormalization, where the codimension-2 properties are inherited from the bulk gravity action.

arXiv comment19 pages, 1 table, 1 figure, typo in eq.(2.8) corrected from published version

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Cited by in corpus (3)

• Holographic renormalization of Horndeski gravity
• Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity
• Dynamical Implementation of the Constraints in Conformal Gravity