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.Comment: 10 pages, No figure, Minor correction

On 3D Minimal Massive Gravity

We study linearized equations of motion of the newly proposed three dimensional gravity, known as minimal massive gravity, using its metric formulation. We observe that the resultant linearized equations are exactly the same as that of TMG by making use of a redefinition of the parameters of the model. In particular the model admits logarithmic modes at the critical points. We also study several vacuum solutions of the model, specially at a certain limit where the contribution of Chern-Simons term vanishes.Comment: 15 pages, no figures, typos fixed, journal versio

Holographic renormalization of 3D minimal massive gravity

We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.Comment: 26 pages, no figures, typos fixed, Ref. adde