Hawking-Page phase transition of Reissner-Nordstrom-de Sitter space-time

Considering the correlation between the black hole and cosmological horizons and regarding the Reissner-Nordstrom-de Sitter (RN-dS) space-time as a thermodynamic system, we discuss the thermodynamic properties of the RN-dS space-time. The behavior of the thermodynamic quantities as the functions x, which is the ratio of the black hole horizon radius to the cosmological horizon radius, is investigated. We find that the coexistent curve of the Hawking-Page (HP) temperature and HP pressure is a closed curve. That means there exist the upper bounds of the HP temperature and HP pressure, which is different from that in AdS black holes. The further investigation of the HP phase transition for RN-dS space-time will help to understand the evolution and microstructure of de Sitter space-time.