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.
Highlights
In the paradigm of de Sitter spacetime, the black hole horizon and the cosmological horizon are always considered to be different thermodynamic systems with different radiation temperatures [20,21,22]
One interesting question arises: considering the possible existence of planar hairy black holes [38,55] and first-order phase transitions in Anti de Sitter (AdS) spacetime [42] once the ground state is correctly identified, is it possible to study the thermodynamic behavior of hairy dS black holes with k = 0? To answer this question, we have studied the behavior of the metric function for planar black holes with k = 0 and hyperbolic black holes with k = −1
Over the past forty years many of the studies in this field have concentrated on the thermodynamics of de Sitter spacetime, in which the black hole horizon and the cosmological horizon are always considered to be different thermodynamic systems with different radiation temperatures [20,21,22]
Summary
In the paradigm of de Sitter spacetime, the black hole horizon and the cosmological horizon are always considered to be different thermodynamic systems with different radiation temperatures [20,21,22]. When the state parameters of charged AdS black holes satisfy certain conditions, the radiation temperature (as well as the effective temperature) of two horizons will be equal to each other [31,32,33] Such constraint condition was extensively discussed in the recent analysis of lukewarm black holes [34], with certain conditions satisfied by the charge of spacetime.
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