Abstract
The entropy of a free scalar field is calculated in the Reissner–Nordström–(anti-)de Sitter spacetimes. Due to the presence of the cosmological horizon in the Reissner–Nordström–de Sitter spacetime, we introduce a cutoff at the cosmological horizon, besides the cutoff at the horizon of black holes in the brick wall model. The entropy is found to be the sum of two terms, which are proportional to the area of the cosmological horizon and of black hole horizon, respectively. In the Reissner–Nordström–anti-de Sitter spacetime the contribution of the anti-de Sitter background to the entropy of scalar fields vanishes when an infinite volume is taken. The entropy of scalar fields is also evaluated in some special backgrounds described by solutions of Einstein–Maxwell equations with a cosmological constant, such as the cold black holes, lukewarm black holes, ultracold solutions, a naked singularity in de Sitter space, and the de Sitter space. The physical meaning of some results is briefly discussed.
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