D-dimensional log gravity

We study Einstein gravity in dimensions D >= 4 modified by curvature squared at critical point where the theory contains only massless gravitons. We show that at the critical point a new mode appears leading to a logarithmic gravity in the theory. The corresponding logarithmic solution may provide a gravity description of logarithmic conformal field theories (CFT) in higher dimensions. We note also that for special values of the parameters of the theory, the model admits solutions with nonrelativistic isometries.