Abstract
Criticality represents a specific point in the parameter space of a higher-derivative gravity theory, where the linearized field equations become degenerate. In 4D Critical Gravity, the Lagrangian contains a Weyl-squared term, which does not modify the asymptotic form of the curvature. The Weyl2 coupling is chosen such that it eliminates the massive scalar mode and it renders the massive spin-2 mode massless. In doing so, the theory turns consistent around the critical point.Here, we employ the Noether–Wald method to derive the conserved quantities for the action of Critical Gravity. It is manifest from this energy definition that, at the critical point, the mass is identically zero for Einstein spacetimes, what is a defining property of the theory. As the entropy is obtained from the Noether–Wald charges at the horizon, it is evident that it also vanishes for any Einstein black hole.
Highlights
General Relativity (GR) is a successful theory of gravity at a classical level but it lacks of consistency in a quantum regime because it is not renormalizable
We provide an alternative formula of conserved charges in Critical Gravity, which makes manifest the fact that the energy for Einstein black holes is
We have shown that, in Critical Gravity, the energy of any Einstein solution vanishes identically
Summary
General Relativity (GR) is a successful theory of gravity at a classical level but it lacks of consistency in a quantum regime because it is not renormalizable. This picture is clearly unphysical as the energy of the perturbations around a background and the mass of a black hole carry opposite signs In view of this general obstruction to obtain a fourdimensional gravity theory which is free of the inconsistencies discussed above, it was quite surprising when the authors of Ref.[8] pointed out the fact that, for the particular couplings α = −3β and β = −1/2Λ, the massive scalar is eliminated and the massive spin-2 mode turns massless. In order to obtain the ADT mass for a general asymptotically AdS (AAdS) solution, we need to write down the metric of the spacetime in the form of gμν = gμν + hμν , where gμν is the metric of the background and hμν is the perturbation tensor Such construction leaves the firstorder variation of field equations as. − α dSν 2ξλ∇ ̄ [μGνL]λ + 2GλL[μ∇ ̄ ν]ξλ
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