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arXiv · 2105.02924

Noether-Wald charges in six-dimensional Critical Gravity

Giorgos Anastasiou·Ignacio J. Araya·Cristobal Corral·Rodrigo Olea
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Abstract

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory -- originally found by Lu, Pang and Pope (LPP) -- can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

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Giorgos Anastasiou, Ignacio J. Araya, Cristobal Corral, Rodrigo Olea. 2021-05-06. Noether-Wald charges in six-dimensional Critical Gravity. https://doi.org/10.1007/jhep07(2021)156

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