Higher-dimensional topological dS black hole with a nonlinear source and its thermodynamics and phase transitions

In this paper, the higher-dimensional topological dS black hole with a nonlinear source (HDTNS) is considered. First, we obtain the thermodynamic quantities of the ( n + 1 )-dimensional topological dS black hole, which satisfy the first law of thermodynamics. Second, based on the effective thermodynamic quantities and Maxwell’s equal-area law method, we explore the phase equilibrium for the HDTNS. The boundary of the two-phase coexistence region in the P eff 0 - T eff 0 diagram is obtained. The critical thermodynamic quantities as well as the horizon potential are also investigated. Furthermore, we analyze the effect of parameters (the spacetime dimension n and the ratio of two horizon radii x = r + / r c ) on the boundary of the two-phase coexistence region and study the latent heat of phase transition for this system, which corresponds to the Clapeyron equation. The results indicate that the phase transition in HDTNS spacetime is analogous to that in a van der Waals (vdW) fluid system, which is determined by electrical potential at the horizon. These results help to understand the fundamental properties of black holes. A more intuitive and profound understanding of gravity is gained by studying the thermodynamic properties of different spacetimes. They provide a theoretical basis for an in-depth study of the classical and quantum properties of de Sitter spacetime and its evolution.