  General Einstein-Gauss-Bonnet gravity with a cosmological constant allows two
(A)dS spacetimes as its vacuum solutions. We find a critical point in the
parameter space where the two (A)dS spacetimes coalesce into one and the
linearized perturbations lack any bilinear kinetic terms. The vacuum
perturbations hence loose their interpretation as linear graviton modes at the
critical point. Nevertheless, the critical theory admits black hole solutions
due to the nonlinear effect. We also consider Einstein gravity extended with
general quadratic curvature invariants and obtain critical points where the
theory has no bilinear kinetic terms for either the scalar trace mode or the
transverse modes. Such critical phenomena are expected to occur frequently in
general higher derivative gravities.
