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arXiv · 2209.02006

Energy functionals from Conformal Gravity

Giorgos Anastasiou·Ignacio J. Araya·Rodrigo Olea
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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.

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Giorgos Anastasiou, Ignacio J. Araya, Rodrigo Olea. 2022-09-05. Energy functionals from Conformal Gravity. https://doi.org/10.1007/jhep10(2022)123

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