Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

Abstract

On the basis of the state parameter of de Sitter space-time satisfying the first law of thermodynamics, we can derive some effective thermodynamic quantities. When the temperature of the black hole horizon is equal to that of the cosmological horizon, we think that the effective temperature of the space-time should have the same value. Using this condition, we obtain a differential equation of the entropy of the de Sitter black hole in the higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective thermodynamic quantities of the de Sitter black hole. The results show that for multi-parameter black holes, the entropy satisfied differential equation is invariable with different independent state parameters. Therefore, the entropy of higher-dimensional dS black holes in dRGT massive gravity is only a function of the position of the black hole horizon, and is independent of other state parameters. It is consistent with the corresponding entropy of the black hole horizon and the cosmological horizon. The thermodynamic quantities of self-consistent de Sitter space-time are given theoretically, and the equivalent thermodynamic quantities have the second-order phase transformation similar to AdS black hole, but unlike AdS black hole, the equivalent temperature of de Sitter space-time has a maximum value. By satisfying the requirement of thermodynamic equilibrium and stability of space-time, the conditions for the existence of dS black holes in the universe are obtained.PACS numbers:

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

“…Considering the interaction between the black hole horizon and the cosmological horizon, we set the entropy of the system [47][48][49]…”

“…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.…”

Thermodynamics of the Reissner-Nordström-de Sitter Spacetime with Quintessence

“…The authors in Refs. [51,52] had shown that when the interaction between the black hole and cosmological horizons of the Reissner-Nordström-de Sitter black hole surrounded by quintessence (RN-dSQ) is considered, the entropy is the summation of the corresponding entropy for two horizons, and together with their interaction term, i.e.…”

Thermodynamics of phase transition in Reissner-Nordstrom-de Sitter spacetime

“…, this result is unacceptable. In recent literatures [52][53][54][55], people consider the interaction between the two horizons, the entropy of RN-dS spacetime is sum of the corresponding entropy of two horizons plus the interaction term, namely…”

“…Exploring the internal relationship between the thermodynamics of different AdS spacetime and dS spacetime black holes not only helps to further understand the entropy, temperature, heat capacity and other properties of black holes, but also has important significance for perfecting the self-consistent black hole thermodynamic geometry theory. In this paper, on the basis of considering the interaction between the black hole horizon and the cosmological horizon to obtain the effective thermodynamic quantity of spacetime [52][53][54][55], the thermodynamic properties of RN-dS spacetime are discussed. The spacetime of RN-dS has the continuous phase transition which is similar to Van de Waals system or charged AdS black hole.…”