Holographic thermodynamics of a charged AdS black holes with global monopole

Abstract: By regarding the Newton constant $G_{N}$ and cosmological constant $\Lambda$ as variables, we in this paper study the thermodynamics and phase transition of Reissner-Nordstr$\ddot{o}$m anti-de Sitter (RN-AdS) black hole with global monopole in the framework of AdS/CFT correspondence. It is found that there are interesting critical phenomena and phase behaviors in the (grand) canonical ensembles of fixed ($\tilde Q,{\cal V},C$), ($\tilde \Phi,{\cal V},C$) and ($\tilde Q,{\cal V},\mu$). When the other parameters are fixed, the free energy decreases with the global monopole increases. In ($\tilde Q,{\cal V},C$) ensemble, the range of unstable region decreases with the increase of global monopole. In ($\tilde \Phi,{\cal V},C$) ensemble, when $\tilde{\Phi} < \Phi_{c}$, the free energy appears two branches, the upper and lower branches correspond to low entropy and high entropy respectively. When ($\tilde Q,{\cal V},\mu$) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain $\mu$-dependent temperatures. When $\mu$ increases to a certain value, this zero-order phase transition disappears. This certain value is negatively related to the magnitude of the global monopole. Finally, we find that $p-\cal V$ criticality does not appear with the change of global monopole. Therefore, it is important to note that the CFT states of charged black holes with global monopole do not correspond to Van der Waals fluids. Finally, we find that charged black holes with global monopoles can better reflect thermodynamic phase transitions and critical phenomena under the AdS/CFT correspondence. By adjusting the change of the global monopole, the thermodynamic phase transition will also change.