  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.

High Energy Physics - Theory;General Relativity and Quantum Cosmology