Hawking–Page phase transition of four-dimensional de-Sitter spacetime with nonlinear source

Abstract

The interplay between a dS black hole horizon and cosmological horizon in a dS spacetime introduces distinctive thermodynamic behaviors (for example the well-known upper bounds of mass and entropy (Dinsmore et al. in Class. Quant. Grav. 37(5), 2020)). Based on this point, we present the Hawking–Page (HP) phase transition of the four-dimensional dS spacetime with nonlinear charge correction when the effective pressure is fixed, and analyze the effects of different effective pressures and nonlinear charge corrections on HP phase transition. The evolution of this system undergoing the HP phase transition is also investigated. We find that the coexistent curve of HP phase transition is a closed one with two different branches. That indicates there exist the upper bounds of the HP temperature and HP pressure, which is completely distinguished with that in AdS spacetime. With decreasing the distance between two horizons, the dS spacetime at the coexistent curve of HP phase transition is going along with different branches. Furthermore, we also explore the influences of charge and nonlinear charge correction on the coexistent curve.