Criticality in Third Order Lovelock Gravity and the Butterfly effect

We study third order Lovelock Gravity in $D=7$ at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in $D=7$ is less than the butterfly velocity for Einstein-Gauss-Bonnet Gravity at the critical point in $D=7$ which is less than the butterfly velocity in D = 7 for Einstein Gravity, $v_{B}^{E.H}>v_{B}^{E.G.B}>v_{B}^{3rd\,\,Lovelock}$. Maybe we can conclude that by adding higher order curvature corrections to Einstein Gravity the butterfly velocity decreases.