Conformal Renormalization of topological black holes in AdS$_6$

TL;DR

This paper demonstrates that Einstein-AdS spaces are solutions within a six-dimensional conformal gravity framework, introducing a conformal renormalization method that simplifies the derivation of Einstein theory actions and applies it to compute black hole thermodynamics.

Contribution

It introduces conformal renormalization as a new method to embed Einstein-AdS solutions into conformal gravity and computes black hole charges using this approach.

Findings

Einstein-AdS spaces are solutions of the conformal gravity in six dimensions.

The action can be expressed as Einstein-Hilbert plus topological and Weyl terms.

Black hole thermodynamic quantities are computed using the new method.

Abstract

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS$_6$ theory.