Conformal Gravity Holography in Four Dimensions

Abstract

We formulate four-dimensional conformal gravity with (Anti-)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown-York stress tensor, the other is a 'partially massless response'. The on-shell action and response functions are finite and do not require holographic renormalization. Finally, we discuss phenomenologically interesting examples, including the most general spherically symmetric solutions and rotating black hole solutions with partially massless hair.

Conserved charges of black holes in Weyl and Einstein–Gauss–Bonnet gravities

“…In the uncharged case, the massM agrees with the one computed from the conserved current that consists of the holographic response functions in [33].…”

“…The mass M N R and the angular momentum J N R in the neutral case coincide with the ones presented in [33]. Next, we consider the conserved charges of the general dyonic rotating black hole (30).…”

New entropy formula for Kerr black holes

“…Similar remarks and results apply to higher spin flat space [32,33] cosmologies [34][35][36]. Let us note for later purposes that in the flat space case the algebra (6) appears naturally in an off-diagonal basis,…”

Holographic stress tensor at finite coupling

“…We expect that for the one, two and three point functions, the simple features we have found in this paper will continue to hold. Finally, it should be possible to extend our methods to study correlation functions which involve the massive graviton modes and T µν [85][86][87].…”