Schottky anomaly of a perturbed Reissner–Nördstrom de Sitter spacetime

For de Sitter spacetime, when the parameters of spacetime satisfy certain conditions, black hole horizon and cosmological horizon coexist in the spacetime. In this region, due to the existence of two horizons with different radiation temperatures, the spacetime does not satisfy the thermodynamic equilibrium stability requirements. This paper considers the spacetime as an overall thermodynamic system and, under the boundary conditions, provides the effective temperature that reflects the entire de Sitter spacetime. Through discussion, it is found that when the effective potential remains unchanged in time, the heat capacity of the de Sitter spacetime exhibits a curve similar to the Schottky specific heat of a two-level system. Moreover, this curve highly coincides with the heat capacity curve when the two horizons are considered as a two-level system. By comparing the maximum values of the heat capacity curves, the number of microscopic particles between the two horizons in the spacetime is estimated. This discovery provides a deeper understanding of de Sitter spacetime. This conclusion opens a new avenue for studying the interactions of microscopic particles inside black holes and simulating the evolution process of the universe, aiming to explore the intrinsic factors driving the accelerated expansion of the universe.