Note on new massive gravity in AdS ₃

In this note we study the properties of linearized gravitational excitations in the new massive gravity theory in asymptotically AdS ₃ spacetime and find that there is also a critical point for the mass parameter at which massive gravitons become massless as in topological massive gravity in AdS ₃. However, at this critical point in the new massive gravity the energy of all branches of highest weight gravitons vanish and the central charges also vanish within the Brown-Henneaux boundary conditions. The new massive gravity in asymptotically AdS ₃ spacetime seems to be trivial at this critical point under the Brown-Henneaux boundary conditions if the Brown-Henneaux boundary conditions can be consistent with this theory. At this point, the boundary conditions of log gravity may be preferred.