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.Comment: 7 pages, no figures, Final version for PL
