Entropy of the electrically charged hairy black holes

Abstract

In this paper, we discuss the effective thermodynamic quantities of higher dimensional electrically charged hairy black holes in de Sitter spacetime, considering the correlation between the black hole horizon and the cosmological horizon. Our results show that, the interaction term determined by the position of the two horizons could significantly contribute to the total entropy of de Sitter spacetime. Moreover, different from the case in AdS spacetime, we find both zero-order and second-order phase transitions under certain conditions, with the absence of first-order phase transition in the electrically charged hairy black holes. These results are strongly supported by the classification of phase transition in Ehrenfest's equations. More interestingly, our analysis demonstrates the validity of the Ehrenfest equations at the critical point, and futhermore indicates the similarity of Prigogine-Defay (PD) ratio between ECBH spacetime and AdS spacetime.

Phase Transition and Entropy Force between Two Horizons in (n+2)-Dimensional de Sitter Space

“…Moreover, the entropy for the interaction between horizons of black holes and the universe is also obtained [13][14][15][16][17]. When we consider the cosmological constant as a thermodynamic state parameter with the thermodynamic pressure, the result shows that de Sitter space not only has a critical behavior similar to the van der Waals system [17,18], but also take second-order phase transition similar to AdS black hole [19][20][21][22][23][24][25][26][27][28][29]. However, the first-order phase transition similar to the AdS black hole is not existing.…”

“…However, thermodynamic systems denoted by the two horizons are not independent, since thermodynamic quantities on them are functions depended on variables of mass M, electric charge Q, and cosmological constant l 2 satisfy the first law of thermodynamics. When parameters of state of (n + 2)-dimensional DRNdS space satisfy the first law of thermodynamics, the entropy is [16][17][18]…”

“…When parameters of state of (n + 2)-dimensional DRNdS space satisfy the first law of thermodynamics, the effective temperature is [16][17][18]…”

“…According to Refs. [16][17][18], a brief review for the effective thermodynamic quantities, the conditions for the phase transition, and the effect of the dimension on the phase transition in (n + 2)-dimensional Reissner-Nordstrom-de Sitter (DRNdS) space is given in the next section. In Section 3, the entropy force of the interaction between horizons of black holes and the universe is derived, and then the effect of the dimension on it is explored.…”

Phase transition and entropic force of de Sitter black hole in massive gravity

“…Therefore dS black holes do not meet the requirements of thermal stability, which brings certain difficulties to the study of the thermodynamic properties of black hole. In recent years, the study of the thermodynamic properties of de Sitter space-time has attracted extensive attention [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Because in the early period of inflation, our universe is a quasi de Sitter space-time, and the constant term introduced in the study of de Sitter space-time is the contribution of vacuum energy, which is also a form of material energy.…”