Hawking-Page Phase Transition of the four-dimensional de-Sitter Spacetime with non-linear source

TL;DR

This paper investigates the Hawking-Page phase transition in four-dimensional de-Sitter spacetime with non-linear charge corrections, revealing unique thermodynamic bounds and the effects of charge and pressure on phase behavior.

Contribution

It introduces the first analysis of Hawking-Page phase transition in dS spacetime with non-linear charge corrections under fixed effective pressure.

Findings

The HP phase transition curve is closed with two branches.

Upper bounds of HP temperature and pressure are identified.

Charge and non-linear corrections influence the coexistent curve.

Abstract

The interplay between a dS black hole and cosmological horizons introduces distinctive thermodynamic behavior in a dS spacetime (for example the well-known upper bounds of mass and entropy in Class. Quant. Grav. 37 (2020) 5). Based on this point, we present the Hawking-Page (HP) phase transition of the four-dimensional dS spacetime with non-linear charge correction when the effective pressure is fixed, and analyze the effects of different effective pressures and non-linear charge corrections on HP phase transition. The evolution of this dS spacetime undergoing the HP phase transition is also investigated. We find that the existent curve of HP phase transition is a closed one with two different branches. That means there exist the upper bounds of the HP temperature and HP pressure, which is completely distinguished with that in AdS spacetime. And with the decreasing of 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 influence of charge and non-linear charge correction on the coexistent curve.