# Influence of inhomogeneities on holographic mutual information and butterfly effect

## TL;DR

This paper investigates how inhomogeneities, introduced via graviton mass in massive gravity, influence mutual information and chaos in a 2+1D field theory, revealing that inhomogeneity and perturbations affect information dynamics.

## Contribution

It explores the impact of inhomogeneity on mutual information and chaos, highlighting the contrasting effects of graviton mass in near- and far-homogeneous regimes.

## Key findings

- Mutual information increases with graviton mass near homogeneity.
- Mutual information decreases with graviton mass far from homogeneity.
- Greater perturbations and inhomogeneity accelerate the disruption of mutual information.

## Abstract

We study the effect of inhomogeneity, which is induced by the graviton mass in massive gravity, on the mutual information and the chaotic behavior of a 2+1-dimensional field theory from the gauge/gravity duality. When the system is near-homogeneous, the mutual information increases as the graviton mass grows. However, when the system is far from homogeneity, the mutual information decreases as the graviton mass increases. By adding the perturbations of energy into the system, we investigate the dynamical mutual information in the shock wave geometry. We find that the greater perturbations disrupt the mutual information more rapidly, which resembles the butterfly effect in chaos theory. Besides, the greater inhomogeneity reduces the dynamical mutual information more quickly just as in the static case.