Realization of Holographic Entanglement Temperature for a Nearly-AdS boundary

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.