Noether-Wald charges in six-dimensional Critical Gravity
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.
Cite
@article{arxiv.2105.02924,
title = {Noether-Wald charges in six-dimensional Critical Gravity},
author = {Giorgos Anastasiou and Ignacio J. Araya and Cristobal Corral and Rodrigo Olea},
journal= {arXiv preprint arXiv:2105.02924},
year = {2021}
}
Comments
16 pages