  Computing the holographic entanglement entropy proposed by Ryu-Takayanagi
shows that thermal energy near boundary region in $AdS_3$ gain maximum of the
temperature. The absolute maxima of temperature is $T^{Max}_{E}= \frac{4G_3
\epsilon_{\infty}}{l}$. By simple physical investigations it has become
possible to predict a phase transition of first order at critical temperature
$T_c\leq T_{E}$. As they predict a tail or root towards which the AdS space
ultimately tend, the boundary is considered thermalized. The Phase transitions
of this form have received striking theoretical and experimental verifications
so far.
