  We study Einstein gravity in dimensions $D\geq 4$ 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 CFT in higher dimensions. We note also that
for special values of the parameters of the theory, the model admits solutions
with non-relativistic isometries.
