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 LΣ. The energy functionals are then particular cases of LΣ 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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Anastasiou, G., Araya, I.J. & Olea, R. Energy functionals from Conformal Gravity. J. High Energ. Phys. 2022, 123 (2022). https://doi.org/10.1007/JHEP10(2022)123
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DOI: https://doi.org/10.1007/JHEP10(2022)123