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 AdS₃ 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 ≤ 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.