# Criticality in Third Order Lovelock Gravity and the Butterfly effect

## TL;DR

This paper investigates the critical behavior of third order Lovelock gravity in seven dimensions, analyzing the butterfly velocity and its relation to higher curvature corrections, revealing that such corrections decrease the butterfly velocity.

## Contribution

It provides the first computation of butterfly velocity at the critical point in third order Lovelock gravity, highlighting the impact of higher curvature terms on chaos propagation.

## Key findings

- Butterfly velocity is non-zero despite no propagating graviton at the critical point.
- Butterfly velocity in third order Lovelock gravity is less than in Einstein-Gauss-Bonnet and Einstein gravity.
- Adding higher order curvature corrections reduces the butterfly velocity.

## Abstract

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.