Abstract
It is well known that de Sitter(dS) black holes generally have a black hole horizon and a cosmological horizon, both of which have Hawking radiation. But the radiation temperature of the two horizons is generally different, so dS black holes do not meet the requirements of thermal equilibrium stability, which brings certain difficulties to the study of the thermodynamic characteristics of black holes. In this paper, dS black hole is regarded as a thermodynamic system, and the effective thermodynamic quantities of the system are obtained. The influence of various state parameters on the effective thermodynamic quantities in the massive gravity space-time is discussed. The condition of the phase transition of the de Sitter black hole in massive gravity space-time is given. We consider that the total entropy of the dS black hole is the sum of the corresponding entropy of the two horizons plus an extra term from the correlation of the two horizons. By comparing the entropic force of interaction between black hole horizon and the cosmological horizon with Lennard-Jones force between two particles, we find that the change rule of entropic force between the two system is surprisingly the same. The research will help us to explore the real reason of accelerating expansion of the universe.
Highlights
Considering whether the corresponding thermodynamic quantity in the de Sitter space-time has the thermodynamic characteristics of AdS black hole after the correlation of black hole horizon and universe horizon; What is the relationship between the entropy of de Sitter space and the corresponding entropy of two horizons? What is the relationship between the entropic force caused by the interaction of two horizons and the ratio of the position of the two horizons? These problems are very important to study the stability and evolution of de Sitter space-time
From formula (13), we know that the total entropy of the effective thermodynamic system in de Sitter black hole in massive gravity (DSBHMG) is divided into two parts, one is the entropy corresponding to the two horizons, and the other term is the increase of the system entropy after considering the interaction of the two horizons as a thermodynamic system, so the entropy is
5 Conclusion and discussion When the black hole horizon and the cosmological horizon are viewed separately as independent thermodynamic systems without considering the correlation between them, the space-time does not meet the requirements of thermodynamic equilibrium stability because the radiation temperature of the two horizons are different
Summary
Since the thermodynamic quantities corresponding to the two horizons in de Sitter space-time are all functions of mass M, charge Q and cosmological constant. There must be certain relation between the thermodynamic quantities corresponding to the two horizons. Considering whether the corresponding thermodynamic quantity in the de Sitter space-time has the thermodynamic characteristics of AdS black hole after the correlation of black hole horizon and universe horizon; What is the relationship between the entropy of de Sitter space and the corresponding entropy of two horizons? What is the relationship between the entropic force caused by the interaction of two horizons and the ratio of the position of the two horizons? These problems are very important to study the stability and evolution of de Sitter space-time. It is worth to establish a self-consistent relationship between
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