Tricritical gravity waves in the four-dimensional generalized massive   gravity
  We construct a generalized massive gravity by combining quadratic curvature gravity with the Chern-Simons term in four dimensions. This may be a candidate for the parity-odd tricritical gravity theory. Considering the AdS$_4$ vacuum solution, we derive the linearized Einstein equation, which is not similar to that of the three dimensional (3D) generalized massive gravity. When a perturbed metric tensor is chosen to be the Kerr-Schild form, the linearized equation reduces to a single massive scalar equation. At the tricritical points where two masses are equal to -1 and 2, we obtain a log-square wave solution to the massive scalar equation. This is compared to the 3D tricritical generalized massive gravity whose dual is a rank-3 logarithmic conformal field theory. 
Taeyoon Moon and Yun Soo Myung
hep-th gr-qc