Effect of massive potentials on the holographic thermalization

We perform a numerical study to recognize the difference between various massive potentials in the dRGT massive gravity on the holographic thermalization in the AdS and AdS Gauss-Bonnet gravities. The massive potential in $4+1$ dimensions includes three symmetric polynomial terms which we denote them as $a_1$, $a_2$ and $a_3$ terms. We observe, in the case of time evolution of entanglement entropy that there is a critical size of the entangling surface on the boundary below which both signs of $a_1$ and above the critical size $a_3$ are able to reduce the thermal value of entanglement entropy. Our numerical computations show the more positive $a_i$'s are, the faster system reaches to its thermal value. The order of saturation time of positive potentials when supplemented to AdS or AdS-GB backgrounds is as $t_{sat}(a_{1})>t_{sat}(a_{2})>t_{sat}(a_{3})$. We also explore these effects on the time evolution of the holographic mutual information.