Holographic thermodynamics of a charged AdS black hole with a global monopole

Abstract

By regarding the Newton constant G N and cosmological constant Λ as variables, in this paper we study the thermodynamics and phase transition of the Reissner-Nordstr öm anti-de Sitter (RN-AdS) black hole with a global monopole within the framework of AdS/CFT correspondence. We find interesting critical phenomena and phase behavior in the (grand) canonical ensembles of fixed ( Q˜,V,C ), ( Φ˜,V,C ) and ( Q˜,V,μ ). When the other parameters are fixed, the free energy decreases with the global monopole increases. In the ( Q˜,V,C ) ensemble, the range of the unstable region decreases with the increase of the global monopole. In the ( Φ˜,V,C ) ensemble, when Φ˜<Φc , the free energy appears as two branches, where the upper and lower branches correspond to low and high entropy, respectively. When ( Q˜,V,μ ) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain μ-dependent temperatures. When μ 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−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 monopoles 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.