Abstract
The density distribution of axion matter on the different black hole background is studied in this article, and some wave function equations are derived on the curve space-time. The density distribution of axion are calculated respectively on the charged black hole and dilaton black hole background. The impact of black hole mass and electric/magnetic charge to the axion density is discussed, and the important role of chemical potential μ for axion density is analyzed. The results show that the density monotonously decreases or oscillation decreases. μ > 0 is corresponding to a high-density superfluid state, and μ < 0 describes a low-density normal state. This means that the axion ordered state of high density may be formed under the black hole background. In addition, the asymptotic correlation function of axion is calculated on a de-Sitter black hole background, and the influence of cosmological constant and chemical potential on the correlation function is also discussed.
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