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

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.